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One-dimensional critical integrable lattice models with a finite-dimensional degree of freedom attached to each lattice site can exhibit the remarkable phenomenon of the emergence of continuous degrees of freedom in the scaling limit. The most studied system in which this occurrence has been observed is the staggered six-vertex model with twisted boundary conditions. Here, we study the influence of different boundary conditions and higher-rank generalisations on/of this model. Our analysis is based on the Bethe ansatz and the formulation of a conserved quantity — the so-called quasi-momentum — which parametrises the non-compact degree of freedom directly on the lattice. Moreover, we carry over the powerful approach of the correspondence between ordinary differential equations and integrable quantum field theories to the case of open boundary conditions. Using this methodology, we can fully classify the scaling limit of the alternating six-vertex model with Uq(sl(2)) boundary conditions. Furthermore, we demonstrate the incompatibility of antidiagonal boundary conditions with a non-compact degree of freedom in the scaling limit. Finally, we provide numerical evidence that the higher rank generalisation, the D(2)3 model, possesses two independent continuous components.

In this note we present some existence results, in the spirit of the celebrated paper by Brezis and Nirenberg (CPAM, 1983), for a perturbed critical problem driven by a mixed local and nonlocal linear operator. We develop an existence theory, both in the case of linear and superlinear perturbations; moreover, in the particular case of linear perturbations we also investigate the mixed Sobolev inequality associated with this problem, detecting the optimal constant, which we show that is never achieved.

© 2001 The American Physical Society. We are thankful for helpful conversations to L. Brey, J. Fontcuberta, G. Gómez-Santos, C. Simon, J. M. de Teresa, and especially to R. Ibarra and V. S. Amaral. V.M.-M. was partially supported by MEC. We acknowledge financial support from Grant Nos. PB96-0875, AEN97-1680, AEN97- 1693, AEN97-1708, AEN99-0990 (MEC, Spain), and (07N/0045/98) (C. Madrid)., It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first- and second-order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational mean-field approach that leads to these results. We also show that the effect of the Berry phase turns out to be crucial to produce first-order paramagnetic-ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a mean-field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the mean-field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins., MEC, Comunidad de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2014 American Physical Society. We thank J. J. Ruiz Lorenzo and E. Marinari for useful discussions. We were partly supported by MINECO, Spain, through the Research Contract No. FIS2012-35719-C02. M.B.J. was supported by the FPU program (MECD, Spain). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant Agreement No. [247328]. The computations were carried out in the GPU-accelerated clusters Tianh-1A (Tianjin, China) and Minotauro (Barcelona, Spain). The total amount of time devoted to this project was 2.2 × 105 GPU hours in Tianhe 1A and 2.0 × 105 GPU hours in Minotauro. Access to Tianhe 1A was granted through Research Contract No. 287746 by the EU-FP7. The authors thankfully acknowledge the computer resources, technical expertise, and assistance provided by the staff at the National Supercomputing Center-Tianjin and at the Red Española de Supercomputación–Barcelona Supercomputing Center., We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark on the presence of strong finite-size effects in the chiral sector. On the spin glass sector, we find that the universality class is that of Ising spin glasses. Our data are compatible with a unique phase transition for the chiral and spin glass sector. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 643 spins, over a vast range of temperatures (hence, of relaxation times)., Unión Europea. FP7, Ministerio de Economía y Competitividad (MINECO), FPU program (MECD, Spain), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2009 The American Physical Society. We acknowledge partial financial support from Ministerio de Ciencia e Innovación Spain through research Contract No. FIS2006-08533., In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4., Ministerio de Ciencia e Innovación, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

It is known that the concept of dissipativeness is fundamental for understanding the asymptotic behavior of solutions to evolutionary problems. In this paper we investigate the dissipative mechanism for some semilinear fourth-order parabolic equations in the spaces of Bessel potentials and discuss some weak conditions that lead to the existence of a compact global attractor. While for second-order reaction-diffusion equations the dissipativeness mechanism has already been satisfactorily understood (see Arrieta et al. (2004), doi:10.1142/S0218202504003234), for higher order problems in unbounded domains it has not yet been fully developed. As shown throughout the paper, one of the main differences from the case of reaction-diffusion equations stems from the lack of a maximum principle. Thus we have to rely here on suitable energy estimates for the solutions. As in the case of second-order reaction-diffusion equations, we show here that both linear and nonlinear terms have to collaborate in order to produce dissipativeness. Thus, the dissipative mechanisms in second-order and fourth-order equations are similar, although the lack of a maximum principle makes the proofs more difficult and the results not as complete. Finally, we make essential use of the sharp results of Cholewa and Rodriguez-Bernal (2012), doi:10.1016/j.na.2011.08.022, on linear fourth-order equations with a very large class of linear potentials., MEC, UCM, Spain., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

©2016 American Physical Society. We are grateful to D. Yllanes and, especially, to L.A. Fernández for substantial help during several parts of this work. We also thank M. Picco and N. Sourlas for reading the manuscript. We were partly supported by MINECO, Spain, through research Contract No. FIS2012-35719-C02-01. Significant allocations of computing time were obtained in the clusters Terminus and Memento (BIFI). N.G.F. acknowledges financial support from a Royal Society Research Grant under No. RG140201 and from a Research Collaboration Fellowship Scheme of Coventry University., It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used., Ministerio de Economía y Competitividad (MINECO), Royal Society (Reino Unido), Coventry University, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1 < p < infinity prove that for a suitable family of Bessel potential spaces, H-p(alpha) (R-N), the linear equation defines a strongly continuous analytic semigroup. Using this result, we prove that the nonlinear problems we consider can be solved for initial data in L-p(RN) and in H-p(2) (R-N). We also find the corresponding critical exponents, that is, the largest growth allowed for the nonlinear terms for these classes of initial data., MEC, UCM, Spain, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

©2015 American Physical Society.We thank Enzo Marinari, Giorgio Parisi, and Andrea Maiorano for helping us with our first Pthreads programs. We also thank Andrea Pelissetto, Giorgio Parisi, and Matteo Lulli for discussing with us, prior to publication, their very interesting and accurate finite-time, finite-size scaling approach [62]. We thank as well Juan Jesus Ruiz-Lorenzo, Peter Young, and David Yllanes for discussions. The total simulation time devoted to this project was the equivalent of 36 days of the full (3072 AMD cores) Memento cluster (see http://bifi.es). We were partly supported by MINECO (Spain) through research Contract No. FIS2012-35719-C02., The statics-dynamics correspondence in spin glasses relate nonequilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ statics-dynamics equivalence to study the Ising spin-glass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature., Ministerio de Economía y Competitividad (MINECO), España, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 1999 IOP Publishing Ltd. We acknowledge interesting discussions with D Stauffer and R Ziff. We thank CICyT (AEN97-1708 and AEN97-1693) for partial financial support. The computations have been carried out using the RTNN machines at Universidad de Zaragoza and Universidad Complutense de Madrid., Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is necessary to put the systematic errors below the statistical ones., CICyT, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2000 The American Physical Society. We gratefully acknowledge discussions with D. Belanger, J. Cardy and H. Rieger. We are grateful for partial financial support from CICyT (AEN97-1708 and AEN97-1693). The computations have been carried out using the RTNN machines (Universidad de Zaragoza and Universidad Complutense de Madrid) and the ORIGIN2000 at the Centro de Supercomputación Complutense (CSC)., We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the secondorder region of its phase diagram. We have found that the n exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the h exponent is definitely different., CICyT, Spain, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

In this paper we show that several known critical exponents for nonlinear parabolic problems axe optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and Cazenave in [9], concerning the behavior of the existence time for critical problems. Our results cover nonlinear heat equations including the case of nonlinear boundary conditions and weigthed spaces settings. In the latter case we show that in some cases the critical exponent is equal to one., DGES (Spain), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We study lattice trees (LTs) and animals (LAs) on the nearest-neighbor lattice Zd in high dimensions. We prove that LTs and LAs display mean-field behavior above dimension 16 and 17 , respectively. Such results have previously been obtained by Hara and Slade in sufficiently high dimensions. The dimension above which their results apply was not yet specified. We rely on the non-backtracking lace expansion (NoBLE) method that we have recently developed. The NoBLE makes use of an alternative lace expansion for LAs and LTs that perturbs around non-backtracking random walk rather than around simple random walk, leading to smaller corrections. The NoBLE method then provides a careful computational analysis that improves the dimension above which the result applies. Universality arguments predict that the upper critical dimension, above which our results apply, is equal to dc= 8 for both models, as is known for sufficiently spread-out models by the results of Hara and Slade mentioned earlier. The main ingredients in this paper are (a) a derivation of a non-backtracking lace expansion for the LT and LA two-point functions; (b) bounds on the non-backtracking lace-expansion coefficients, thus showing that our general NoBLE methodology can be applied; and (c) sharp numerical bounds on the coefficients. Our proof is complemented by a computer-assisted numerical analysis that verifies that the necessary bounds used in the NoBLE are satisfied.

We study lattice trees (LTs) and animals (LAs) on the nearest-neighbor lattice Zd in high dimensions. We prove that LTs and LAs display mean-field behavior above dimension 16 and 17 , respectively. Such results have previously been obtained by Hara and Slade in sufficiently high dimensions. The dimension above which their results apply was not yet specified. We rely on the non-backtracking lace expansion (NoBLE) method that we have recently developed. The NoBLE makes use of an alternative lace expansion for LAs and LTs that perturbs around non-backtracking random walk rather than around simple random walk, leading to smaller corrections. The NoBLE method then provides a careful computational analysis that improves the dimension above which the result applies. Universality arguments predict that the upper critical dimension, above which our results apply, is equal to dc= 8 for both models, as is known for sufficiently spread-out models by the results of Hara and Slade mentioned earlier. The main ingredients in this paper are (a) a derivation of a non-backtracking lace expansion for the LT and LA two-point functions; (b) bounds on the non-backtracking lace-expansion coefficients, thus showing that our general NoBLE methodology can be applied; and (c) sharp numerical bounds on the coefficients. Our proof is complemented by a computer-assisted numerical analysis that verifies that the necessary bounds used in the NoBLE are satisfied.

We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value., SCOPUS: ar.j, info:eu-repo/semantics/published

We give necessary and sufficient conditions for the existence of positive radial solutions for a class of fully nonlinear uniformly elliptic equations posed in the complement of a ball in RN, and equipped with homogeneous Dirichlet boundary conditions., SCOPUS: ar.j, info:eu-repo/semantics/published

We report on some recent results obtained for positive radial solutions of Lane-Emden-Fowler type equations with Pucci's operators as principal parts. The presented results include the asymptotic analysis of almost critical solutions in the unit ball, existence results in annular domains and sharp Liouville-type results for exterior Dirichlet problems.

The thermodynamic limit of superspin chains can show several intriguing properties, including the emergence of continua of scaling dimensions and the appearance of discrete states when imposing toroidal boundary conditions. Nevertheless, the former’s exhaustive characterization in terms of Conformal Field Theories is still lacking. In order to study the thermodynamic limit of the U_q[sl(2|1)] 3 ⊗ 3̄ superspin chain in the antiferromagnetic regime, we analyze the low lying excitations by means of the model’s exact solution using the Algebraic Bethe Ansatz. In the isotropic limit, this model may be used as a toy model for the description of plateau transitions in Quantum Hall systems. The definition of a quasimomentum operator allows for a characterization of the continua of scaling dimensions, thereby giving rise to a quantum number for the corresponding non-compact component of the spectrum in the thermodynamic limit. The associated degeneracies are lifted on the lattice by logarithmic fine structures. Based on the extrapolation of our finite size data we find that under a variation of the boundary conditions from periodic to antiperiodic for the fermionic degrees of freedom, levels from the continuous part of the spectrum flow into discrete levels and vice versa. Investigating the thermodynamic limit of the q-deformed osp(3|2) superspin chain, corresponding to an intersecting loop model in the rational limit, we seek to uncover its low-lying critical exponents. We present evidences that the latter are built in terms of composites of anomalous dimensions of two Coulomb gases with distinct radii and exponents associated to Z(2) degrees of freedom. This view is supported by the fact that the S = 1 XXZ integrable chain spectrum is present in some of the sectors of the superspin chain at a particular value of the deformation parameter. We find that the fine structure of finite-size effects is very rich for a typical anisotropic spin chain. In fact, we argue on the exist

In this expository paper we present a list of different semilinear wave-type problems with time-variable coefficients. The aim of this work is to understand the influence of such coefficients on the critical exponents for polynomial nonlinearities. Statements of global existence and blow-up will follow according to exponents which are below or above these critical ones.

© 2017 American Physical Society. We thank the staff of the BIFI supercomputing center for their assistance and for computing time at the cluster Memento. This work was partially supported by MINECO (Spain) through Grant No. FIS2015-65078-C2-1-P. We thank the Royal Society International Exchanges Scheme 2016/R1 for supporting N.G.F. and M.P. N.G.F. is grateful to Coventry University for providing support through a Research Sabbatical Fellowship during which part of this work has been completed., The random-field Ising model is one of the few disordered systems where the perturbative renormalization group can be carried out to all orders of perturbation theory. This analysis predicts dimensional reduction, i.e., that the critical properties of the random-field Ising model in D dimensions are identical to those of the pure Ising ferromagnet in D − 2 dimensions. It is well known that dimensional reduction is not true in three dimensions, thus invalidating the perturbative renormalization group prediction. Here, we report high-precision numerical simulations of the 5D random-field Ising model at zero temperature. We illustrate universality by comparing different probability distributions for the random fields. We compute all the relevant critical exponents (including the critical slowing down exponent for the ground-state finding algorithm), as well as several other renormalization-group invariants. The estimated values of the critical exponents of the 5D random-field Ising model are statistically compatible to those of the pure 3D Ising ferromagnet. These results support the restoration of dimensional reduction at D = 5. We thus conclude that the failure of the perturbative renormalization group is a low-dimensional phenomenon. We close our contribution by comparing universal quantities for the random-field problem at dimensions 3 ≤ D < 6 to their values in the pure Ising model at D − 2 dimensions, and we provide a clear verification of the Rushbrooke equality at all studied dimensions., Ministerio de Economía y Competitividad (MINECO), Royal Society International Exchanges Scheme, Coventry University, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Traditionally the study of the magnetocaloric effect (MCE) in amorphous and nanocrystalline alloys has been focused on Fe and rare earth based compositions. However, they present problems that hinder their application such as the high price of rare earths or the necessary addition of a large fraction of non-magnetic elements in Fe-based alloys in order to tune their response to temperatures close to room temperature. Alternatively, Ni-based amorphous alloys have the Curie temperature (T) well below room temperature and with a good glass forming ability. For these alloys, Fe addition provides a good tool to tune T close to room temperature. In this work, the magnetocaloric properties of NiFeSiB (x = 8, 12, 13.2, 16) have been studied in the amorphous and nanocrystalline state. Besides compositional dependence of MCE in this series, a detailed analysis of the critical exponents of the magnetic transition of both amorphous and nanocrystalline alloys has been performed using the magnetic field dependence of MCE. Results were compared with those derived from the Kouvel-Fisher method, requiring a deconvolution of the different magnetization contributions in the Kouvel-Fisher case for nanocrystalline alloys.

The critical exponent for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114-116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.

The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein et al. (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.

Treball final de màster oficial fet en col·laboració amb Universitat Autònoma de Barcelona (UAB), Universitat de Barcelona (UB) i Institut de Ciències Fotòniques (ICFO), Bose-Einstein condensates display quantum phase transitions that cannot be explained with a mean field theory. Describing each trap as an effective site of a Bose-Hubbard model and using the Schwinger representation the system can be mapped onto spin models. We show that it is possible to define correlations between bosons in such a way that critical behaviour is associated to the divergence of a correlation length accompanied by a gapless spectrum in the thermodynamic limit. Such description provides critical exponents and encompasses the notion of universality.

We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in L-q(Omega) for each 1 <= q <= infinity. In particular, we do not assume restriction on the growth of the nonlinearites required by the standar local existence theory., MEC, UCM Spain, EU, EPSRC, UK, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Due to the lack of the maximum principle the analysis of higher order parabolic problems in RN is still not as complete as the one of the second-order reaction-diffusion equations. While the critical exponents and then a dissipative mechanism in the subcritical case have already been satisfactorily described (see Cholewa and Rodriguez-Bernal (2012)), for problems in the critical or supercritical regime the questions concerning well or illposedness, as well as possible dissipative properties of the solutions, have not yet been satisfactorily answered. This article is devoted to the analysis of the higher order parabolic problems in R-N in the latter case. Focusing on the critical and supercritical regimes we give sufficient "good"-sign conditions proving that the problem is then globally well posed in L-2(R-N) and even possesses a compact global attractor. On the other hand, for supercritically growing "bad"-signed nonlinearities we show that the problem is ill-posed., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations., Originally published in dissertation in manuscript form.

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations., Originally published in dissertation in manuscript form.

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations., Originally published in dissertation in manuscript form.

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations., Originally published in dissertation in manuscript form.

We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless disks at fixed packing fraction phi in two dimensions. We use these distributions to address the question of how pressure increases as phi increases above the jamming point phi(J), p similar to |phi - phi(J) |(y). For statically jammed ensembles, our results are consistent with the exponent y being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of y is consistent with a nontrivial value, as found previously in rheological simulations., Originally published in dissertation in manuscript form.

© 2013 American Physical Society. We were partly supported by MICINN, Spain, through research contracts No. FIS2009-12648-C03 and No. FIS2012-35719-C02-01. Significant allocations of computing time were obtained in the clusters Terminus and Memento (BIFI). We are grateful to D. Yllanes and, especially, to L. A. Fernández for substantial help during several parts of this work. We also thank A. Pelissetto and G. Tarjus for useful correspondence., We solve a long-standing puzzle in statistical mechanics of disordered systems. By performing a high-statistics simulation of the D = 3 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correction-to-scaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections., Ministerio de Ciencia e Innovación (MICINN), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian cortex, one type of complex dynamics that spontaneously emerges from neuronal interactions has been characterized as neuronal avalanches. Several aspects of neuronal avalanches such as their size and life time distributions are described by power laws with unique exponents, indicating an underlying critical branching process that governs avalanche formation. Here, we show that neuronal avalanches also reflect an organization of brain dynamics close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing a control parameter equivalent to thermodynamic temperature, we observed typical critical behavior in cortical activities near the actual physiological condition, including the phase transition of an order parameter, as well as the divergence of susceptibility and specific heat. Finite-size scaling of these quantities allowed us to derive robust critical exponents highly consistent across monkey and humans that uncover a distinct, yet universal organization of brain dynamics. Our results demonstrate that normal brain dynamics at rest resides near or at criticality, which maximizes several aspects of information processing such as input sensitivity and dynamic range.

Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian cortex, one type of complex dynamics that spontaneously emerges from neuronal interactions has been characterized as neuronal avalanches. Several aspects of neuronal avalanches such as their size and life time distributions are described by power laws with unique exponents, indicating an underlying critical branching process that governs avalanche formation. Here, we show that neuronal avalanches also reflect an organization of brain dynamics close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing a control parameter equivalent to thermodynamic temperature, we observed typical critical behavior in cortical activities near the actual physiological condition, including the phase transition of an order parameter, as well as the divergence of susceptibility and specific heat. Finite-size scaling of these quantities allowed us to derive robust critical exponents highly consistent across monkey and humans that uncover a distinct, yet universal organization of brain dynamics. Our results demonstrate that normal brain dynamics at rest resides near or at criticality, which maximizes several aspects of information processing such as input sensitivity and dynamic range.

Thermodynamic criticality describes emergent phenomena in a wide variety of complex systems. In the mammalian cortex, one type of complex dynamics that spontaneously emerges from neuronal interactions has been characterized as neuronal avalanches. Several aspects of neuronal avalanches such as their size and life time distributions are described by power laws with unique exponents, indicating an underlying critical branching process that governs avalanche formation. Here, we show that neuronal avalanches also reflect an organization of brain dynamics close to a thermodynamic critical point. We recorded spontaneous cortical activity in monkeys and humans at rest using high-density intracranial microelectrode arrays and magnetoencephalography, respectively. By numerically changing a control parameter equivalent to thermodynamic temperature, we observed typical critical behavior in cortical activities near the actual physiological condition, including the phase transition of an order parameter, as well as the divergence of susceptibility and specific heat. Finite-size scaling of these quantities allowed us to derive robust critical exponents highly consistent across monkey and humans that uncover a distinct, yet universal organization of brain dynamics. Our results demonstrate that normal brain dynamics at rest resides near or at criticality, which maximizes several aspects of information processing such as input sensitivity and dynamic range.

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

In general, tumors exhibit irregular borders with geometrical properties which are expected to depend upon their degree of malignancy. To appropriately evaluate these irregularities, it is necessary to apply segmentation procedures on the image that clearly define the active region of the tumor and its border. In the present work, nosologic maps were obtained combining T2-weighted magnetic resonance images with in vivo magnetic resonance spectroscopy information on brain tumors. The image was segmented according to the nosologic map and tumor contours were determined. Several fractal properties were determined on the contour: the capacity or fractal dimension, the correlation dimension for a temporal series constructed from the original contour, and also a critical exponent coming from the contour roughness. The results obtained showed a good correlation between the roughness critical exponent and the degree of malignancy of the tumor.

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

In this work, a study of the nematic (N)-isotropic (I) phase transition has been made in a series of odd non-symmetric liquid crystal dimers, the alpha-(4-cyanobiphenyl-4'-yloxy)-omega-(1-pyrenimine-benzylidene-4'-oxy) alkanes, by means of accurate calorimetric and dielectric measurements. These materials are potential candidates to present the elusive biaxial nematic (N-B) phase, as they exhibit both molecular biaxiality and flexibility. According to the theory, the uniaxial nematic (N-U)-isotropic (I) phase transition is first-order in nature, whereas the N-B-I phase transition is second-order. Thus, a fine analysis of the critical behavior of the N-I phase transition would allow us to determine the presence or not of the biaxial nematic phase and understand how the molecular biaxiality and flexibility of these compounds influences the critical behavior of the N-I phase transition.

We consider the critical spread-out contact process in Z^d with d ≥ 1, whose infection range is denoted by L ≥ 1. In this paper, we investigate the higher-point functions τ^(r)_ t^^→ (x^^→) for r ≥ 3, where τ^(r)_ t^^→ (x^^→) is the probability that, for all i = 1, . . . , r − 1, the individual located at x_i ∈ Z^d is infected at time t_i by the individual at the origin o ∈ Z^d at time 0. Together with the results of the 2-point function in [16], on which our proofs crucially rely, we prove that the r-point functions converge to the moment measures of the canonical measure of super-Brownian motion above the upper critical dimension 4. We also prove partial results for d ≤ 4 in a local mean-field setting. The proof is based on the lace expansion for the time-discretized contact process, which is a version of oriented percolation in Z^d × ԑZ_+, where ԑ ∈ (0,1] is the time unit. For ordinary oriented percolation (i.e., ԑ = 1), we thus reprove the results of [20]. The lace expansion coefficients are shown to obey bounds uniformly in ԑ ∈ (0,1], which allows us to establish the scaling results also for the contact process (i.e., ǫ ↓ 0). We also show that the main term of the vertex factor V, which is one of the non-universal constants in the scaling limit, is 2 − ԑ (= 1 for oriented percolation, = 2 for the contact process), while the main terms of the other non-universal constants are independent of ԑ.

This paper considers Hardy-Lieb-Thirring inequalities for higher order differential operators. A result for general fourth-order operators on the half-line is developed, and the trace inequality tr((-Delta)(2)-C(d,2)(HR)1/vertical bar x vertical bar(4)-V(x))(-)(gamma)<= C-gamma integral V-Rd(x)(+)(gamma+d/4)dx, gamma >= 1 - d/4, where C-d,2(HR) the sharp constant in the Hardy-Rellich inequality and where C-gamma > 0 is independent of V. is proved for dimensions d = 1, 3. As a corollary of this inequality, a Sobolev-type inequality is obtained., QC 20110103

Using a new elementary method, we prove the existence of minimizers for various critical problems in BV(Omega) and also in W-1,W-P(Omega), 1 < p < infinity. (C) 2010 Elsevier Inc. All rights reserved.

Vorliegende Diplomarbeit befasst sich mit der Simulation von Spin-Modellen auf Nvidia Grafikkarten. Hierbei wird das Programmiermodell CUDA verwendet, welches einer breiten Masse von Softwareentwicklern den Zugang zu GPGPU (General Purpose Computation on Graphics Processing Units) gestattet ohne dass diese notwendigerweise mit (massiv) paralleler Programmierung vertraut sein müssen. Im Rahmen von Vergleichen der Programmlaufzeiten für Simulationen des Ising- Modells sowie des Ising-Spin-Glases auf Nvidia Tesla C1060 Grafikkarten und einer Intel Core i7-920 x86 Quad-Core-CPU war zu vermerken, dass, abhängig vom konkreten Modell und der Rechengenauigkeit (32-bit oder 64-bit), die Tesla C1060 zwischen 5-10 mal schneller arbeitete als die Core i7-920 Quad-Core-CPU. Wir haben uns ebenfalls mit der Zuverlässigkeit von GPGPU-Rechnungen befasst, gerade in Hinblick auf das Auftreten von Soft-Errors, wie es in [23] angedeutet wird. Wir beobachteten falsche Programmausgaben bei langen Simulationen des Ising-Modells auf ,,großen'''' Gittern. Es gelang uns die auftretenden Probleme mit Überhitzung der entsprechenden Grafikkarten in Verbindung zu bringen. Für die Durchführung von Monte-Carlo-Simulationen auf Parallelrechnerarchitekturen, wie es in vorliegender Arbeit der Fall ist, liegt es nahe auch Zufallszahlen parallel zu erzeugen. Wir präsentieren Implementierungen der Zufallszahlengeneratoren Ranlux und Mersenne Twister. Zusätzlich stellen wir eine alternative und sehr effiziente Möglichkeit vor parallele Zufallszahlen auf Nvidia Grafikkarten zu erzeugen. Alle verwendeten Zufallszahlengeneratoren wurden erfolgreich auf ihre Qualität getestet indem Monte-Carlo-Schätzer exakten Rechnungen gegenübergestellt wurden., This thesis reports on simulating spin models on Nvidia graphics cards using the CUDA programming model; a particular approach for making GPGPU (General Purpose Computation on Graphics Processing Units) available for a wide range of software developers not necessarily acquainted with (massively) parallel programming. By comparing program execution times for simulations of the Ising model and the Ising spin glass by means of the Metropolis algorithm on Nvidia Tesla C1060 graphics cards and an Intel Core i7-920 quad-core x86 CPU (we used OpenMP to make our simulations run on all 4 execution units of the CPU), we noticed that the Tesla C1060 performed about a factor 5-10 faster than the Core i7-920, depending on the particular model and the accuracy of the calculations (32-bit or 64-bit). We also investigated the reliability of GPGPU computations, especially with respect to the occurrence of soft-errors as suggested in [23]. We noticed faulty program outputs during long-time simulations of the Ising model on ''large'' lattices. We were able to link these problems to overheating of the corresponding graphics cards. Doing Monte Carlo simulations on parallel computer architectures, as was the case in this thesis, suggests to also generate random numbers in a parallel manner. We present implementations of the random number generators Ranlux and Mersenne Twister. In addition, we give an alternative and very efficient approach for producing parallel random numbers on Nvidia graphics cards. We successfully tested all random number generators used in this thesis for their quality by comparing Monte Carlo estimates against exact calculations.

Vorliegende Diplomarbeit befasst sich mit der Simulation von Spin-Modellen auf Nvidia Grafikkarten. Hierbei wird das Programmiermodell CUDA verwendet, welches einer breiten Masse von Softwareentwicklern den Zugang zu GPGPU (General Purpose Computation on Graphics Processing Units) gestattet ohne dass diese notwendigerweise mit (massiv) paralleler Programmierung vertraut sein müssen. Im Rahmen von Vergleichen der Programmlaufzeiten für Simulationen des Ising- Modells sowie des Ising-Spin-Glases auf Nvidia Tesla C1060 Grafikkarten und einer Intel Core i7-920 x86 Quad-Core-CPU war zu vermerken, dass, abhängig vom konkreten Modell und der Rechengenauigkeit (32-bit oder 64-bit), die Tesla C1060 zwischen 5-10 mal schneller arbeitete als die Core i7-920 Quad-Core-CPU. Wir haben uns ebenfalls mit der Zuverlässigkeit von GPGPU-Rechnungen befasst, gerade in Hinblick auf das Auftreten von Soft-Errors, wie es in [23] angedeutet wird. Wir beobachteten falsche Programmausgaben bei langen Simulationen des Ising-Modells auf ,,großen'''' Gittern. Es gelang uns die auftretenden Probleme mit Überhitzung der entsprechenden Grafikkarten in Verbindung zu bringen. Für die Durchführung von Monte-Carlo-Simulationen auf Parallelrechnerarchitekturen, wie es in vorliegender Arbeit der Fall ist, liegt es nahe auch Zufallszahlen parallel zu erzeugen. Wir präsentieren Implementierungen der Zufallszahlengeneratoren Ranlux und Mersenne Twister. Zusätzlich stellen wir eine alternative und sehr effiziente Möglichkeit vor parallele Zufallszahlen auf Nvidia Grafikkarten zu erzeugen. Alle verwendeten Zufallszahlengeneratoren wurden erfolgreich auf ihre Qualität getestet indem Monte-Carlo-Schätzer exakten Rechnungen gegenübergestellt wurden., This thesis reports on simulating spin models on Nvidia graphics cards using the CUDA programming model; a particular approach for making GPGPU (General Purpose Computation on Graphics Processing Units) available for a wide range of software developers not necessarily acquainted with (massively) parallel programming. By comparing program execution times for simulations of the Ising model and the Ising spin glass by means of the Metropolis algorithm on Nvidia Tesla C1060 graphics cards and an Intel Core i7-920 quad-core x86 CPU (we used OpenMP to make our simulations run on all 4 execution units of the CPU), we noticed that the Tesla C1060 performed about a factor 5-10 faster than the Core i7-920, depending on the particular model and the accuracy of the calculations (32-bit or 64-bit). We also investigated the reliability of GPGPU computations, especially with respect to the occurrence of soft-errors as suggested in [23]. We noticed faulty program outputs during long-time simulations of the Ising model on ''large'' lattices. We were able to link these problems to overheating of the corresponding graphics cards. Doing Monte Carlo simulations on parallel computer architectures, as was the case in this thesis, suggests to also generate random numbers in a parallel manner. We present implementations of the random number generators Ranlux and Mersenne Twister. In addition, we give an alternative and very efficient approach for producing parallel random numbers on Nvidia graphics cards. We successfully tested all random number generators used in this thesis for their quality by comparing Monte Carlo estimates against exact calculations.

The relation between the interlayer exchange coupling and magnetic order is addressed, using Fe/V(0 0 1) superlattices as a model system. Large decrease in the ordering temperature (Tc) is observed with decreasing interlayer exchange coupling. The effective exponents of the magnetization were determined to be larger than 0.5 for all the samples, which is strongly deviating from the classical values of both two- and three-dimensional systems. This effect can partially be ascribed to the presence of boundaries, invoked by the finite number of magnetic layers.

A large-scale Monte Carlo simulation study of the Ising model for the simple cubic lattice was recently performed by us. In this paper, we complement that study with the bcc, fcc and diamond lattices. Both the canonical and microcanonical ensembles are employed. We give estimates of the critical temperature and also other quantities in the critical region. An analysis of the critical behaviour points to distinct high-and low-temperature exponents, especially for the specific heat, as was also obtained for the simple cubic lattice, although the agreement is good between the different lattices. The source of this discrepancy is briefly discussed., QC 20100525

A large-scale Monte Carlo simulation study of the Ising model for the simple cubic lattice was recently performed by us. In this paper, we complement that study with the bcc, fcc and diamond lattices. Both the canonical and microcanonical ensembles are employed. We give estimates of the critical temperature and also other quantities in the critical region. An analysis of the critical behaviour points to distinct high-and low-temperature exponents, especially for the specific heat, as was also obtained for the simple cubic lattice, although the agreement is good between the different lattices. The source of this discrepancy is briefly discussed.