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Triplet-triplet annihilation (TTA) in phosphorescent emission layers of modern organic light-emitting diodescompromises their performance and device lifetime. TTA can occur by a Förster-type interaction between twotriplets, leading to a loss of one of them. The TTA process gives rise to correlations in the positions of thesurviving triplets, which complicate its study. These correlations can in principle be accounted for exactly inkinetic Monte Carlo (KMC) simulations, but such simulations are computationally expensive. Here, we presentmaster equation modeling of TTA that accounts for correlations in a computationally efficient way. Cases withoutand with triplet diffusion, which partly washes out correlations, are considered. We calculate the influence ofTTA on transient photoluminescence experiments, where it leads to a deviation from exponential decay, and onsteady-state emission efficiency. A comparison with KMC simulations shows that our master equation modelingis an accurate and computationally competitive alternative.

The generalization of the Dyson Brownian Motion approach of random matrices to Anderson Localization (AL) models [Chalker, Lerner and Smith PRL 77, 554 (1996)] and to Many-Body Localization (MBL) Hamiltonians [Serbyn and Moore arxiv:1508.07293] is revisited to extract the level repulsion exponent $\beta$, where $\beta=1$ in the delocalized phase governed by the Wigner-Dyson statistics, $\beta=0$ in the localized phase governed by the Poisson statistics, and $0 |^2 $ for the same eigenstate $m=n$ and for consecutive eigenstates $m=n+1$. For the Anderson Localization tight-binding Hamiltonian with random on-site energies $h_i$, we find $\beta =2 Y_{n,n+1}(N)/(Y_{n,n}(N)-Y_{n,n+1}(N)) $ in terms of the Density Correlation matrix $Y_{nm}(N) \equiv \sum_{i=1}^N | < \phi_n | i> |^2 | |^2 $ for consecutive eigenstates $m=n+1$, while the diagonal element $m=n$ corresponds to the Inverse Participation Ratio $Y_{nn}(N) \equiv \sum_{i=1}^N | < \phi_n | i> |^4 $ of the eigenstate $| \phi_n>$., Comment: 22 pages

A Fully Many-Body Localized (FMBL) quantum disordered system is characterized by the emergence of an extensive number of local conserved operators that prevents the relaxation towards thermal equilibrium. These local conserved operators can be seen as the building blocks of the whole set of eigenstates. In this paper, we propose to construct them explicitly via some block real-space renormalization. The principle is that each RG step diagonalizes the smallest remaining blocks and produces a conserved operator for each block. The final output for a chain of $N$ spins is a hierarchical organization of the $N$ conserved operators with $\left(\frac{\ln N}{\ln 2}\right)$ layers. The system-size nature of the conserved operators of the top layers is necessary to describe the possible long-ranged order of the excited eigenstates and the possible critical points between different FMBL phases. We discuss the similarities and the differences with the Strong Disorder RSRG-X method that generates the whole set of the $2^N$ eigenstates via a binary tree of $N$ layers. The approach is applied to the Long-Ranged Quantum Spin-Glass Ising model, where the constructed excited eigenstates are found to be exactly like ground states in another disorder realization, so that they can be either in the paramagnetic phase, in the spin-glass phase or critical., 11 pages

The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling $J(r) \propto r^{-1-\sigma}$ in the region $1/2, Comment: 14 pages, 2 figures

We consider the Dyson hierarchical version of the quantum Spin-Glass with random Gaussian couplings characterized by the power-law decaying variance $\overline{J^2(r)} \propto r^{-2\sigma}$ and a uniform transverse field $h$. The ground state is studied via real-space renormalization to characterize the spinglass-paramagnetic zero temperature quantum phase transition as a function of the control parameter $h$. In the spinglass phase $h, Comment: 9 pages, 7 figures

In the first part of this paper, we derive the general replica equations that describe infinite-dimensional hard spheres at any level of replica symmetry breaking (RSB) and in particular in the fullRSB scheme. We show that these equations are formally very similar to the ones that have been derived for spin glass models, thus showing that the analogy between spin glasses and structural glasses conjectured by Kirkpatrick, Thirumalai, and Wolynes is realized in a strong sense in the mean field limit. We also suggest how the computation could be generalized in an approximate way to finite dimensional hard spheres. In the second part of the paper, we discuss the solution of these equations and we derive from it a number of physical predictions. We show that, below the Gardner transition where the 1RSB solution becomes unstable, a fullRSB phase exists and we locate the boundary of the fullRSB phase. Most importantly, we show that the fullRSB solution predicts correctly that jammed packings are isostatic, and allows one to compute analytically the critical exponents associated with the jamming transition, which are missed by the 1RSB solution. We show that these predictions compare very well with numerical results.

We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip dynamics near zero temperature, we construct via real-space renormalization the full hierarchy of relaxation times of the master equation for any given realization of the random couplings. We then analyze the probability distribution of dynamical barriers as a function of the spatial scale. This real-space renormalization procedure represents a simple explicit example of the droplet scaling theory, where the convergence towards local equilibrium on larger and larger scales is governed by a strong hierarchy of activated dynamical processes, with valleys within valleys., v2=final version

The presence of a random magnetic field in ferromagnetic systems leads, in the broken phase, to an anomalous $O(\sqrt{1/N})$ convergence of some thermodynamic quantities to their asymptotic limits. Here we show a general method, based on the replica trick, to compute analytically the $O(\sqrt{1/N})$ finite size correction to the average free energy. We apply this method to two mean field Ising models, fully connected and random regular graphs, and compare the results to exact numerical algorithms. We argue that this behaviour is present in finite dimensional models as well.

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed., 42 pages, 19 figures. Minor changes and added figure (results unchanged)

We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections. QC 20150625

We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial conditions. We use the Bethe Ansatz solution for the replicated problem which is an attractive bosonic model. The problem is more difficult than the previous solution of the fixed endpoint problem as it requires regularization of the spatial integrals over the Bethe eigenfunctions. We use either a large fixed system length or a small finite slope KPZ initial conditions (wedge). The latter allows to take properly into account non-trivial contributions, which appear as deformed strings in the former. By considering a half-space model in a proper limit we obtain an expression for the generating function of all positive integer moments $\bar{Z^n}$ of the directed polymer partition function. We obtain the generating function of the moments of the DP partition sum as a Fredholm Pfaffian. At large time, this Fredholm Pfaffian, valid for all time $t$, exhibits convergence of the free energy (i.e. KPZ height) distribution to the GOE Tracy Widom distribution, Comment: 62 pages

In this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: critical line, behavior of the principal thermodynamic observables and their fluctuations as well as overlap fluctuations are obtained and discussed. Then, we move further, extending such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two quenched spin glass free energies even in the replica symmetric framework. © 2012 IOP Publishing Ltd and SISSA Medialab srl.

We study the 3D Edwards-Anderson spin glasses, by analyzing spin-spin correlation functions in thermalized spin configurations at low T on large lattices. We consider individual disorder samples and analyze connected clusters of very correlated sites: we analyze how the volume and the surface of these clusters increases with the lattice size. We qualify the important excitations of the system by checking how large they are, and we define a correlation length by measuring their gyration radius. We find that the clusters have a very dense interface, compatible with being space filling., 9 pages, 4 figures. Version accepted for publication

In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the spherical $s+p$-spin glass model, extending the work of Barrat, Franz and Parisi J. Phys. A 30, 5593 (1997). We confirm the presence of level crossings, bifurcations, and temperature chaos. For the states that are at equilibrium close to the so-called dynamical temperature $T_d$, we find, however, that the following state method (and the dynamical solution of the model as well) is intrinsically limited by the vanishing of solutions with non-zero overlap at low temperature.

The first theoretical study of a dimer adsorption process at a homogeneous surface is presented. By using the RSA algorithm, we show example monolayers, discuss estimations of random jamming coverages and measure the surface blocking function, which could be used for calculating real systems kinetics. We also find the correlation function for coverages generated and analyse the orientational ordering inside the adsorbed monolayer. The results are compared with theoretical and experimental data.

We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and link density low enough), where spins are long range correlated, even if the ground states energy stiffness is null. In other words, in this region twisting the boundary conditions cost no energy, but spins are long range correlated by means of pure entropic effects., Comment: 15 pages, 6 figures. v3: added a phase diagram for ferromagnetically biased couplings

We study the superfluid-to-Bose glass transition in a disordered Bose-Hubbard model through a very simple variational wavefunction: a permanent of non-orthogonal single-particle wavefunctions that are variationally determined. The transition is identified by the behavior of the superfluid stiffness. We also introduce a less rigorous but very enlightening criterium for the transition, which is related to the overlap matrix among the single-particle wavefunctions that are used to built the permanent. We find that the two criteria agree quite well. We finally consider a further quantity, the bipartite entanglement entropy, which also provides a good estimator for the superfluid-to-Bose glass transition., 23 pages, 6 figures, final version

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes currently exploited in order to generate the expected topology are based on a-priori assumptions and in most cases still implement constant intensities for links. Here we propose a simple shift in the definition of patterns in an Hopfield model to convert frustration into dilution: By varying the bias of the pattern distribution, the network topology -which is generated by the reciprocal affinities among agents - crosses various well known regimes (fully connected, linearly diverging connectivity, extreme dilution scenario, no network), coupled with small world properties, which, in this context, are emergent and no longer imposed a-priori. The model is investigated at first focusing on these topological properties of the emergent network, then its thermodynamics is analytically solved (at a replica symmetric level) by extending the double stochastic stability technique, and presented together with its fluctuation theory for a picture of criticality. At least at equilibrium, dilution simply decreases the strength of the coupling felt by the spins, but leaves the paramagnetic/ferromagnetic flavors unchanged. The main difference with respect to previous investigations and a naive picture is that within our approach replicas do not appear: instead of (multi)-overlaps as order parameters, we introduce a class of magnetizations on all the possible sub-graphs belonging to the main one investigated: As a consequence, for these objects a closure for a self-consistent relation is achieved., 30 pages, 4 figures

We investigate the evolution of a population of non-interacting particles which undergo diffusion and multiplication. Diffusion is assumed to be homogeneous, while multiplication proceeds with different rates reflecting the distribution of nutrients. We focus on the situation where the distribution of nutrients is a stationary quenched random variable, and show that the population exhibits a super-exponential growth whenever the nutrient distribution is unbounded. We elucidate a huge difference between the average and typical asymptotic growths and emphasize the role played by the spatial correlations in the nutrient distribution., 15 pages, 1 figure

We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range character of correlations is translated into a broad distribution of the spin-spin correlation coefficients for almost all realizations of the random couplings. When we sample the whole phase space we find that this distribution is so broad indeed that at low temperatures it essentially becomes uniform, with all possible correlation values appearing with the same probability. The distribution of correlations inside a single phase space valley is also studied and found to be much narrower., Added a few references and a comment phrase

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations., 48 pages, 19 postscript figures, 9 tables. Version accepted for publication in the Journal of Statistical Mechanics

We study the solutions of Von Neumann's expanding model with reversible processes for an infinite reaction network. We show that, contrary to the irreversible case, the solution space need not be convex in contracting phases (i.e. phases where the concentrations of reagents necessarily decrease over time). At optimality, this implies that, while multiple dynamical paths of global contraction exist, optimal expansion is achieved by a unique time evolution of reaction fluxes. This scenario is investigated in a statistical mechanics framework by a replica symmetric theory. The transition from a non-convex to a convex solution space, which turns out to be well described by a phenomenological order parameter (the fraction of unused reversible reactions) is analyzed numerically., 13+epsilon pages

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "mean-field approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures., Comment: 12 pages, 6 figures

We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class., Comment: 11 pages, 4 figures

The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may stem. In order to make theoretical immunology appealing to the statistical physicist audience we are going to work out a research article which, from one side, may hopefully act as a benchmark for future improvements and developments, from the other side, it is written in a very pedagogical way both from a theoretical physics viewpoint as well as from the theoretical immunology one. Furthermore, we have chosen to test our model describing a wide range of features of the adaptive immune response in only a paper: this has been necessary in order to emphasize the benefit available when using disordered statistical mechanics as a tool for the investigation. However, as a consequence, each section is not at all exhaustive and would deserve deep investigation: for the sake of completeness, we restricted details in the analysis of each feature with the aim of introducing a self-consistent model., Comment: 22 pages, 14 figure

We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including disordered and topologically inhomogenous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and it can be consistently extended as a local temperature when far from equilibrium. This holds for homogeneous as well as for disordered systems. In particular, we will consider a system characterized by ferromagnetic random couplings $J_{ij} \in [ 1 - \epsilon, 1 + \epsilon ]$. We show that the dynamics relaxes to steady states, and that heat transport can be described on the average by means of a Fourier equation. The presence of disorder reduces the conductivity, the effect being especially appreciable for low temperatures. We finally discuss a possible singular behaviour arising for small disorder, i.e. in the limit $\epsilon \to 0$., Comment: 14 pages, 8 figures

Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with kappa=4 whereas their fractal dimension is d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution" (SLE). Optimal droplets with a lateral size between L and 2L have the same fractal dimension as domain walls but an energy that saturates at a value of order O(1) for L->infinity such that arbitrarily large excitations exist which cost only a small amount of energy. Finally it is demonstrated that the sensitivity of the ground state to small changes of order delta in the disorder is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations of the perturbed ground state with the unperturbed ground state, rescaled by the roughness, are suppressed and approach zero logarithmically., 23 pages, 11 figures

Commentary on `Asymptotic statistics of the n-sided planar Poisson–Voronoi cell: II. Heuristics', by H J Hilhorst, 2009 J. Stat. Mech. P05007.

We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the authors in Prog. Theor. Phys. 111, 661 (2004). The expression can be handled both analytically and numerically, which is useful for examining how the analyticity of the moment with respect to the replica numbers, which play the role of powers of the moment, can be broken in the thermodynamic limit. A comparison with a replica method analysis indicates that the analyticity breaking can be regarded as the origin of the one-step replica symmetry breaking. The validity of the expression is also confirmed by numerical methods for finite systems., 16 pages, 4 figures

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential., 18 pages, 8 figures; Fig. 8 improved adding results for another value of q (q=830/1076)

complete version to be found in JPA; International audience; Assuming energy states to be an independent and identically distributed positive sequence, a randomized version of the conventional Bose occupancy problem is investigated.

We study the purely relaxational dynamics (model A) at criticality in three-dimensional disordered Ising systems whose static critical behaviour belongs to the randomly diluted Ising universality class. We consider the site-diluted and bond-diluted Ising models, and the +- J Ising model along the paramagnetic-ferromagnetic transition line. We perform Monte Carlo simulations at the critical point using the Metropolis algorithm and study the dynamic behaviour in equilibrium at various values of the disorder parameter. The results provide a robust evidence of the existence of a unique model-A dynamic universality class which describes the relaxational critical dynamics in all considered models. In particular, the analysis of the size-dependence of suitably defined autocorrelation times at the critical point provides the estimate z=2.35(2) for the universal dynamic critical exponent. We also study the off-equilibrium relaxational dynamics following a quench from T=\infty to T=T_c. In agreement with the field-theory scenario, the analysis of the off-equilibrium dynamic critical behavior gives an estimate of z that is perfectly consistent with the equilibrium estimate z=2.35(2)., 38 pages

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, $\nu=0.683(2)$, $\eta=0.036(1)$, $\alpha=-0.049(6)$, $\gamma=1.341(4)$, $\beta=0.354(1)$, $\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $\omega=0.33(3)$ and $\omega_2=0.82(8)$., Comment: 45 pages, 22 figs, revised estimate of nu

Within the framework of Von Neumann's expanding model, we study the maximum growth rate r achievable by an autocatalytic reaction network in which reactions involve a finite (fixed or fluctuating) number D of reagents. r is calculated numerically using a variant of the Minover algorithm, and analytically via the cavity method for disordered systems. As the ratio between the number of reactions and that of reagents increases the system passes from a contracting (r1). These results extend the scenario derived in the fully connected model ($D\to\infinity$), with the important difference that, generically, larger growth rates are achievable in the expanding phase for finite D and in more diluted networks. Moreover, the range of attainable values of r shrinks as the connectivity increases., 20 pages

We present results of a Monte Carlo study of the equilibrium dynamics of the one dimensional long-range Ising spin glass model. By tuning a parameter $\sigma$, this model interpolates between the mean field Sherrington-Kirkpatrick model and a proxy of the finite dimensional Edward-Anderson model. Activated scaling fits for the behavior of the relaxation time $\tau$ as a function of the number of spins $N$ (Namely $\ln(\tau)\propto N^{\psi}$) give values of $\psi$ that are not stable against inclusion of subleading corrections. Critical scaling ($\tau\propto N^{\rho}$) gives more stable fits, at least in the non mean field region. We also present results on the scaling of the time decay of the critical remanent magnetization of the Sherrington-Kirkpatrick model, a case where the simulation can be done with quite large systems and that shows the difficulties in obtaining precise values for dynamical exponents in spin glass models.

We investigate a disordered version of a thermodynamic fiber bundle model proposed by Selinger, Wang, Gelbart, and Ben-Shaul a few years ago. For simple forms of disorder, the model is analytically tractable and displays some new features. At either constant stress or constant strain, there is a non monotonic increase of the fraction of broken fibers as a function of temperature. Moreover, the same values of some macroscopic quantities as stress and strain may correspond to different microscopic cofigurations, which can be essential for determining the thermal activation time of the fracture. We argue that different microscopic states may be characterized by an experimentally accessible analog of the Edwards-Anderson parameter. At zero temperature, we recover the behavior of the irreversible fiber bundle model., 18 pages, 10 figures

By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by the system during its evolution are distributed according to a multinomial probability density. The class includes i) the uniformly fully connected models, namely a collection of states all connected with equal hopping coefficients and in the presence of a potential operator with arbitrary levels and degeneracies, and ii) the random potential systems, in which the hopping operator is generic and arbitrary potential levels are assigned randomly to the states with arbitrary probabilities. For this class of models we find a universal thermodynamic limit characterized only by the levels of the potential, rescaled by the ground-state energy of the system for zero potential, and by the corresponding degeneracies (probabilities). If the degeneracy (probability) of the lowest potential level tends to zero, the ground state of the system undergoes a quantum phase transition between a normal phase and a frozen phase with zero hopping energy. In the frozen phase the ground state condensates into the subspace spanned by the states of the system associated with the lowest potential level., 31 pages, 13 figures

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak., Comment: 8 pages, 1 figure

We apply path-integral techniques to study the dynamics of agent-based models with asymmetric information structures. In particular, we devise a batch version of a model proposed originally by Berg et al. [Quant. Fin. 1 (2001) 203], and convert the coupled multi-agent processes into an effective-agent problem from which the dynamical order parameters in ergodic regimes can be derived self-consistently together with the corresponding phase structure. Our dynamical study complements and extends the available static theory. Results are confirmed by numerical simulations., minor revision of text, accepted by JSTAT

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear lattice defects is not applicable - still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena., Comment: Journal of Statistical Mechanics: Theory and Experiment, 2015, P02011

We present a method derived by cavity arguments to compute the spin-glass and higher-order susceptibilities in diluted mean-field spin-glass models. The divergence of the spin-glass susceptibility is associated to the existence of a non-zero solution of a homogeneous linear integral equation. Higher order susceptibilities, relevant for critical dynamics through the parameter exponent $\lambda$, can be expressed at criticality as integrals involving the critical eigenvector. The numerical evaluation of the corresponding analytic expressions is discussed. The method is illustrated in the context of the de Almeida-Thouless line for a spin-glass on a Bethe lattice but can be generalized straightforwardly to more complex situations., Comment: v3: typo error in eq. (10) (and similar equations) corrected

We study the performance of different message passing algorithms in the two dimensional Edwards Anderson model. We show that the standard Belief Propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a Generalized Belief Propagation (GBP) algorithm, derived from a Cluster Variational Method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: Double Loop (DL) and a two-ways message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to non paramagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude., Comment: 19 pages, 13 figures

During the last years, through the combined effort of the insight, coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features of the mean field Sherrington-Kirkpatrick spin glass model have been firmly established. In particular, it has been possible to prove the existence and uniqueness of the infinite volume limit for the free energy, and its Parisi expression, in terms of a variational principle, involving a functional order parameter. Even the expected property of ultrametricity, for the infinite volume states, seems to be near to a complete proof. The main structural feature of this model, and related models, is the deep phenomenon of spontaneous replica symmetry breaking (RSB), discovered by Parisi many years ago. By expanding on our previous work, the aim of this paper is to investigate a general frame, where replica symmetry breaking is embedded in a kind of mechanical scheme of the Hamilton-Jacobi type. Here, the analog of the "time" variable is a parameter characterizing the strength of the interaction, while the "space" variables rule out quantitatively the broken replica symmetry pattern. Starting from the simple cases, where annealing is assumed, or replica symmetry, we build up a progression of dynamical systems, with an increasing number of space variables, which allow to weaken the effect of the potential in the Hamilton-Jacobi equation, as the level of symmetry braking is increased. This new machinery allows to work out mechanically the general K-step RSB solutions, in a different interpretation with respect to the replica trick, and lightens easily their properties as existence or uniqueness., Comment: 24 pages, no figures

What is the origin of the sharp slowdown displayed by glassy systems? Physical common sense suggests there must be a concomitant growing correlation length, but finding this length has been nontrivial. In random first-order theory, it is given by the size of amorphous excitations, which depends on a balance between their mutual interfacial energy and their configurational entropy. But how these excitations disappear when crossing over to the normal high temperature phase is unclear, chiefly due to lack of data about the surface tension. We measure the energy cost for creating amorphous excitations in a model glass-former, and discover that the surface tension vanishes at a well-defined spinodal energy, above which amorphous excitations cannot be sustained. This spinodal therefore marks the true onset of glassiness., Facultad de Ciencias Exactas, Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas

In this paper we obtain two results for the Sherrington-Kirkpatrick (SK) model, and we show that they both emerge from a single approach. First, we prove that the average of the overlap takes positive values when it is non zero. More specificly, the average of the overlap, which is naively expected to take values in the whole interval $[-1,+1]$, becomes positive if we ``first'' apply an external field, so to destroy the gauge invariance of the model, and ``then'' remove it in the thermodynamic limit. This phenomenon emerges at the critical point. This first result is weaker that the one obtained by Talagrand (not limited to the average of the overlap), but we show here that, at least in average, the overlap is proven to be non-negative with no use of the Ghirlanda-Guerra identities. The latter are instead needed to obtain the second result, which is the control the behavior of the overlap at the critical point: we find the critical exponents of all the overlap correlation functions., Comment: 19 pages