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Intrinsically random hardware devices are increasingly attracting attention for their potential use in probabilistic computing architectures. One such device is the single-photon avalanche diode (SPAD) and an associated functional unit, the variable-rate SPAD circuit (VRSC), recently proposed by us as a source of randomness for sampling and annealing Ising and Potts models. This work develops a more advanced understanding of these VRSCs by introducing several VRSC design options and studying their tradeoffs as implemented in a 65-nm CMOS process. Each VRSC is composed of a SPAD and a processing circuit. Combinations of three different SPAD designs and three different types of processing circuits were evaluated on several metrics such as area, speed, and variability. Measured results from the SPAD design space show that even extremely small SPADs are suitable for probabilistic computing purposes, and that high dark count rates are not detrimental either, so SPADs for probabilistic computing are actually easier to integrate in standard CMOS processes. Results from the circuit design space show that the time-to-analog-based designs introduced in this work can produce highly exponential and analytical transfer functions, but that the less analytically tractable output of the previously proposed filter-based designs can achieve less variability in a smaller footprint. Probabilistic bits (P-bits) composed of the fabricated VRSCs achieve bit flip rates of 50 MHz and allow at least one order of magnitude of control over their simulated annealing temperature.

• UAV acquired images were collected to count wheat spikes under three different scenarios. • APW: an ensemble model was proposed for efficient recognition of wheat spikes. • The spikes identification results of Potts model were calculated through ADMM model. • Watershed model was used to segment the overlapping wheat spikes. • Compared to benchmarked algorithm (ITS), APW have more recognition accuracy. The accurate estimation of wheat ear is of great significance to gain high yield for ensuring food security. The use of computer vision for wheat ear counting to improve the estimation efficiency and accuracy has been explored by many scholars. However, existing single-computer vision recognition methods have insufficient robustness and recognition of adherent wheat ears. This study mainly focused on to solve the problem of adherent wheat ears, and proposed a combined algorithm called "APW" that ensemble with alternating direction methods of multipliers (ADMM), Potts algorithm and Watershed to achieve fast recognition and counting of wheat ears. The images of wheat ears were collected under three different scenarios including growth stages, planting densities, and flight heights by using unmanned aerial vehicle (UAV), and the Potts model was used to recognise the images. The masked images of the wheat ear were converted into a greyscale image, and were layered using a greyscale gradient. Finally, the watershed algorithm was used to segment adherent wheat ears in the layered image, and the centroids were labelled and counted. The results shows that the best accuracy was obtained under low planting density scenario, with an R2 of 0.89 and a root mean square error (RMSE) of 3.72, suggesting that APW can handle scenarios with large background differences and low target adherence. These findings provides a new approach for efficient counting of wheat ears in UAV acquired images. [ABSTRACT FROM AUTHOR]

Abstract The paper tackles the problem of joint deconvolution and segmentation of textured images. The images are composed of regions containing a patch of texture that belongs to a set of K possible classes. Each class is described by a Gaussian random field with parametric power spectral density whose parameters are unknown. The class labels are modelled by a Potts field driven by a granularity coefficient that is also unknown. The method relies on a hierarchical model and a Bayesian strategy to jointly estimate the labels, the K textured images in addition to hyperparameters: the signal and the noise levels as well as the texture parameters and the granularity coefficient. The capability to estimate the latter is an important feature of the paper. The estimates are designed in an optimal manner as a risk minimizer that yields the marginal posterior maximizer for the labels and the posterior mean for the rest of the unknowns. They are computed based on a convergent procedure from samples of the posterior obtained through an advanced MCMC algorithm: Perturbation-Optimization step and Fisher Metropolis-Hastings step within a Gibbs loop. Various numerical evaluations provide encouraging results despite the strong difficulty of the problem.

The present study aimed to investigate the clinical effects of the brand new perioperative transfusion trigger score (POTTS) system in patients undergoing malignant tumor surgeries. 442 cases of patients diagnosed with malignant tumor were randomly selected (from January 2012 to December 2016) from Zunyi Medical University and were divided into 3 experimental groups. Patients in the POTTS group were transfused by the POTTS guideline perioperatively, while patients in the 7–10 g group were treated by the traditional transfusion guidelines existed (restrictive transfusion strategy), patients in the 10 g group should be transfused to keep the Hb level no less than 10 g/dL (liberal transfusion strategy). Baseline information, operation time, bleeding volume, transfusion amount, incision healing time, postoperative complications, metastasis and recurrence were observed and recorded. Postoperative short-term mortality was comparable of the 3 groups, 3 cases of death all occurred in 10 g group, there was no significant difference in the incidence of postoperative complications, including infectious complications and coagulation related complications. Follow-up to date, there were 25 cases, 29 cases and 29 cases of tumor recurrence and metastasis in the three groups, but no statistical difference observed. The present findings show that the POTTS transfusion system is more advantageous with regard to save blood and relieve economic burdens of patients, and does not affect the long-term recurrence and metastasis rate of malignant tumor. [ABSTRACT FROM AUTHOR]

Intrinsically random hardware devices are increasingly attracting attention for their potential use in probabilistic computing architectures. One such device is the single-photon avalanche diode (SPAD) and an associated functional unit, the variable-rate SPAD circuit (VRSC), recently proposed by us as a source of randomness for sampling and annealing Ising and Potts models. This work develops a more advanced understanding of these VRSCs by introducing several VRSC design options and studying their tradeoffs as implemented in a 65-nm CMOS process. Each VRSC is composed of a SPAD and a processing circuit. Combinations of three different SPAD designs and three different types of processing circuits were evaluated on several metrics such as area, speed, and variability. Measured results from the SPAD design space show that even extremely small SPADs are suitable for probabilistic computing purposes, and that high dark count rates are not detrimental either, so SPADs for probabilistic computing are actually easier to integrate in standard CMOS processes. Results from the circuit design space show that the time-to-analog-based designs introduced in this work can produce highly exponential and analytical transfer functions, but that the less analytically tractable output of the previously proposed filter-based designs can achieve less variability in a smaller footprint. Probabilistic bits (P-bits) composed of the fabricated VRSCs achieve bit flip rates of 50 MHz and allow at least one order of magnitude of control over their simulated annealing temperature.

We study the orientation of rods in the neighborhood of a surface. A semi-infinite region in two different situations is considered: (i) the rods are located close to a flat wall and (ii) the rods occupy the space that surrounds a sphere. In a recent paper we investigated a similar problem: the interior of a sphere, with a fixed concentration of rods. Here, we allow for varying concentration, the rods are driven from a reservoir to the neighborhood of the surface by means of a tunable chemical potential. In the planar case, the particle dimensions are irrelevant. In the curved case, we consider cylinders with dimensions comparable to the radius of curvature of the sphere; as they come close to the surface, they have to accommodate to fill the available space, leading to a rich orientational profile. These systems are studied by a mapping onto a three-state Potts model with annealed disorder on a semi-infinite lattice; two order parameters describe the system: the occupancy and the orientation. The Hamiltonian is solved using a mean-field approach producing recurrence relations that are iterated numerically and we obtain various interesting results: the system undergoes a first order transition just as in the bulk case; the profiles do not have a smooth decay but may present a step and we search for the factors that determine their shape. The prediction of such steps may be relevant in the field of self-assembly of colloids and nanotechnology.

We formulate measures of spin ordering in the q -state ferromagnetic Potts model in a generalized external magnetic field that favors or disfavors spin values in a subset I s = { 1 , ... , s } of the total set of q values. The results are contrasted with the corresponding measures of spin ordering in the case of a conventional external magnetic field that favors or disfavors a single spin value out of total set of q values. Some illustrative calculations are included. [ABSTRACT FROM AUTHOR]

Abstract: Through Monte Carlo simulations we study the 2D Potts models with and states on Voronoi–Delaunay random lattice. In this study, we assume that the coupling factor varies with the distance between the first neighbors as , with . The disordered system is simulated by applying the single-cluster Monte Carlo update algorithm and the reweighting technique. In this model both second-order and first-order phase transitions are present depending on values and parameter. The critical exponents’ ratios , and were calculated for the case where the second-order phase transitions are present. In the Potts model with we also studied the distribution of cluster sizes. [Copyright &y& Elsevier]

The zero-temperature Glauber dynamics is used to investigate the persistence probability P(t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, ..., 230 states on directed and undirected Barabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i.e., P(∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, ..., 230; this shows "blocking" for all these Q values. Except that for Q = 230 in the undirected case P(t) tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins. [ABSTRACT FROM AUTHOR]

Abstract: Monte Carlo (MC) simulations, finite-size scaling and theoretical analysis have been carried out to study the critical behavior of long linear particles of length (-mers) on honeycomb lattices. A nematic phase, characterized by a big domain of parallel -mers, is separated from the isotropic state, by a continuous transition occurring at a finite density . Our study allowed: (1) to determine the minimum value of (), which allows the formation of the nematic phase, being ; (2) to predict the dependence of on , being ; and (3) to obtain the critical exponents, which indicate that the transition belongs to the 2D three-state Potts universality class. [Copyright &y& Elsevier]

We identify a conformal field theory (CFT) that describes the Yang–Lee edge singularity of the 2-dimensional (2D) 3-state Potts model. The identification is based on a comparison of finite-size scaling measurements to predictions for conformal minimal models. The comparison shows that the Yang–Lee edge singularities of the 2D 3-state Potts and the 2D Ising models are in the same universality class. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of multiband image clustering and segmentation. We propose a new methodology for doing this, called model-based cluster trees. This is grounded in model-based clustering, which bases inference on finite mixture models estimated by maximum likelihood using the EM algorithm, and automatically chooses the number of clusters by Bayesian model selection, approximated using BIC, the Bayesian Information Criterion. For segmentation, model-based clustering is based on a Markov spatial dependence model. In the Markov model case, the Bayesian model selection criterion takes account of spatial neighborhood information, and is termed PLIC, the Pseudolikelihood Information Criterion. We build a cluster tree by first segmenting an image band, then using the second band to cluster each of the level 1 clusters, and continuing if required for further bands. The tree is pruned automatically as a part of the algorithm by using Bayesian model selection to choose the number of clusters at each stage. An efficient algorithm for implementing the methodology is proposed. An example is used to evaluate this new approach, and the advantages and disadvantages of alternative approaches to multiband segmentation and clustering are discussed. [Copyright &y& Elsevier]

: We consider the optimal paths in a d-dimensional lattice, where the bonds have isotropically correlated random weights. These paths can be interpreted as the ground state configuration of a simplified polymer model in a random potential. We study how the universal scaling exponents, the roughness and the energy fluctuation exponent, depend on the strength of the disorder correlations. Our numerical results using Dijkstra's algorithm to determine the optimal path in directed as well as undirected lattices indicate that the correlations become relevant if they decay with distance slower than 1/r in d = 2 and 3. We show that the exponent relation 2ν - ω = 1 holds at least in d = 2 even in case of correlations. Both in two and three dimensions, overhangs turn out to be irrelevant even in the presence of strong disorder correlations. [ABSTRACT FROM AUTHOR]

: Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the system is strongly anisotropic, the shape dependence in space-time enters through the effective aspect ratio reff = ct/Lz, where c is a non-universal constant and z the anisotropy exponent. A particular attention is paid to the influence of the initial state on the universal behaviour of the crossing probability. Using anisotropic finite-size scaling and generalizing a simple argument given by Aizenman for isotropic percolation, we also obtain the behaviour of the probability to find n incipient spanning clusters on a finite system at time t. The numerical results are in good agreement with the conjecture. [ABSTRACT FROM AUTHOR]

: The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. [ABSTRACT FROM AUTHOR]

: Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N2 bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N2. The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q3. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. [ABSTRACT FROM AUTHOR]

: Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of improving the molecular field approximation by inserting spin clusters of variable sizes into a homogeneously magnetised background. The density of states of these spin clusters is then computed exactly. We show that the true non-classical critical exponents can be extracted from spin clusters treated in such a manner. For this purpose a molecular field finite size scaling theory is discussed and effective critical exponents are analysed. Reliable values of critical quantities of various Ising and Potts models are extracted from very small system sizes. [ABSTRACT FROM AUTHOR]

The density of never changed opinions during the Sznajd consensus-finding process decays with time t as 1/ tθ. We find θ ≃ 3/8 for a chain, compatible with the exact Ising result of Derrida et al. In higher dimensions, however, the exponent differs from the Ising θ. With simultaneous updating of sublattices instead of the usual random sequential updating, the number of persistent opinions decays roughly exponentially. Some of the simulations used multi-spin coding. [ABSTRACT FROM AUTHOR]

To investigate the performance of the energy landscape paving (ELP) procedure for peptides, we apply it here to deltorphin, a linear heptapeptide with bulky side chains (H-Tyr1-D-Met2-Phe3-His4-Leu5-Met6-Asp7-NH2) and compare the results with the Multicanonical method (MUCA) in regard of finding the low-energy structures. Deltorphin is modeled in vacuum by the potential energy function ECEPP. [ABSTRACT FROM AUTHOR]

We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average connectivity ( z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient of the 1/ z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking. The 1/ z expansion is well defined also in the zero temperature limit. [ABSTRACT FROM AUTHOR]

We study the behavior of a hydrophobic chain near a hydrophobic boundary in two dimensions, adapting the decorated lattice model of Berkema and Widom (G.T. Barkema, B. Widom, J. Chem. Phys. 113, 2349 (2000)) to obtain effective, temperature-dependent intrachain and chain-boundary interactions. We use these interactions to construct two model Hamiltonians. The resulting partition functions may be integrated numerically. Our results compare favorably with preliminary Monte Carlo computations, using the same effective interactions. At relatively low temperatures and at high temperatures, we find that the chain is randomly configured in the ambient water, and detached from the wall, whereas at intermediate temperatures it adsorbs onto the wall in a stretched or partially folded state, again depending upon the temperature, and the energy of solvation. [ABSTRACT FROM AUTHOR]

We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem. [ABSTRACT FROM AUTHOR]

The random field q-states Potts model is investigated using exact groundstates and finite-temperature transfer matrix calculations. It is found that the domain structure and the Zeeman energy of the domains resembles for general q the random field Ising case ( q = 2). This is also the expected outcome based on a random-walk picture of the groundstate. The domain size distribution is exponential, and the scaling of the average domain size with the disorder strength is similar for q arbitrary. The zero-temperature properties are compared to the equilibrium spin states at small temperatures, to investigate the effect of local random field fluctuations that imply locally degenerate regions. The response to field perturbations (`chaos') and the susceptibility are investigated. In particular for the chaos exponent it is found to be 1 for q = 2,..., 5. Finally for q = 2 (Ising case) the domain length distribution is studied for correlated random fields. [ABSTRACT FROM AUTHOR]

Motivated by recent experiments on cuprates with low-dimensional magnetic interactions, a new class of two-dimensional Ising models with short-range interactions and mobile defects is introduced and studied. The non-magnetic defects form lines, which, as temperature increases, first meander and then become unstable. Using Monte Carlo simulations and analytical low- and high-temperature considerations, the instability of the defect stripes is monitored for various microscopic and thermodynamic quantities in detail for a minimal model, assuming some of the couplings to be indefinitely strong. The robustness of the findings against weakening the interactions is discussed as well. [ABSTRACT FROM AUTHOR]

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C( l, t) ≈ lα f ( t/ lα/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. [ABSTRACT FROM AUTHOR]

Few years ago, application of the mean field Bethe scheme on a given system was shown to produce a systematic change of the system intrinsic symmetry. For instance, once applied on a ferromagnet, individual spins are no more equivalent. Accordingly a new loopwise mean field theory was designed to both go beyond the one site Weiss approach and yet preserve the initial Hamitonian symmetry. This loopwise scheme is applied here to solve the triangular antiferromagnetic Ising model. It is found to yield Wannier's exact result of no ordering at non-zero temperature. No adjustable parameter is used. Simultaneously a non-zero critical temperature is obtained for the triangular Ising ferromagnet. This simple mean field scheme opens a new way to tackle random systems. [ABSTRACT FROM AUTHOR]

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. We discuss physical applications to systems with annealed and quenched disorder. Examples are the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n = 0, that usually goes along with an application of the replica trick. [ABSTRACT FROM AUTHOR]

Generalized multifractal formalism is used to study singularity spectra of strongly inhomogeneous multifractals characterized by coarse-grained probability measures with zero minimal and/or infinite maximal Hölder exponents. Due to involving two additional types of scaling indices, the generalized formalism is shown to be able to describe complex multifractal objects by families of bivariate spectra rather than familiar single spectra of singularity strengths of one type, providing a more complete and adequate characteristics of such objects. It is proved that the families of extended singularity spectra can reveal unusual forms with many maxima, reflecting complex scaling structures of strongly inhomogeneous multifractals. [ABSTRACT FROM AUTHOR]

A model to terrorism is presented using the theory of percolation. Terrorism power is related to the spontaneous formation of random backbones of people who are sympathetic to terrorism but without being directly involved in it. They just don't oppose in case they could. In the past such friendly-to-terrorism backbones have been always existing but were of finite size and localized to a given geographical area. The September 11 terrorist attack on the US has revealed for the first time the existence of a world wide spread extension. It is argued to have result from a sudden world percolation of otherwise unconnected and dormant world spread backbones of passive supporters. The associated strategic question is then to determine if collecting ground information could have predict and thus avoid such a transition. Our results show the answer is no, voiding the major criticism against intelligence services. To conclude the impact of military action is discussed. [ABSTRACT FROM AUTHOR]

Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents are determined in two and higher dimensions. The local persistence exponent obeys a scaling relation involving the order parameter exponent of the absorbing phase transition. Furthermore we observe that the global persistence exponent exceeds its local counterpart in all dimensions in contrast to the known persistence behavior in reversible phase transitions. [ABSTRACT FROM AUTHOR]

The dynamics of spreading of the minority opinion in public debates (a reform proposal, a behavior change, a military retaliation) is studied using a diffusion reaction model. People move by discrete step on a landscape of random geometry shaped by social life (offices, houses, bars, and restaurants). A perfect world is considered with no advantage to the minority. A one person-one argument principle is applied to determine locally individual mind changes. In case of equality, a collective doubt is evoked which in turn favors the Status Quo. Starting from a large in favor of the proposal initial majority, repeated random size local discussions are found to drive the majority reversal along the minority hostile view. Total opinion refusal is completed within few days. Recent national collective issues are revisited. The model may apply to rumor and fear propagation. [ABSTRACT FROM AUTHOR]

The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality [ABSTRACT FROM AUTHOR]

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value dc = 3 below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit d = 1 is reached. This mechanism is analyzed numerically for the Ising model with d ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality. [ABSTRACT FROM AUTHOR]

Random walk arguments and exact numerical computations are used to study one-dimensional random field chains. The ground state structure is described with absorbing and non-absorbing random walk excursions. At low temperatures, the local magnetization follows the ground state except at regions where a local random field fluctuation makes thermal excitations easier. This is explained by the random walk picture, implying that the magnetization lengthscale is a product of the domain size and the thermal excitation scale. [ABSTRACT FROM AUTHOR]

The effect of surface on the critical behaviour of a ferromagnetic Ising spin model in a random transverse surface and bulk fields is studied by the use of an effective field method within the framework of a single-site cluster theory. The state equations are derived using a probability distribution method based on the use of Van der Waerden identities. The complete phase diagrams are investigated when the transverse fields are bimodally and trimodally distributed. In particular, the influence of the transverse fields, exchange interaction strength ratio and the distribution parameter on the phase diagrams behaviour is examined in detail. [ABSTRACT FROM AUTHOR]

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for Sz = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. [ABSTRACT FROM AUTHOR]

We study the statistical properties of the sum St = dt'σ t', that is the difference of time spent positive or negative by the spin σ t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of St and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( T > Tc), criticality ( T = Tc), and low temperature ( T < Tc). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents ( x), in the low temperature phase. The probability that the temporal mean St/ t was always larger than the equilibrium magnetization is found to decay as t- - ½. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model. [ABSTRACT FROM AUTHOR]

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece [2,3] which show that two of these parameters, G and Gc, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass ( p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for Tc and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at. [ABSTRACT FROM AUTHOR]

The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the n = 0 limit allows one to discuss the renormalization group properties in spite of this phenomenon. The attraction of pairs of replicas is enhanced under renormalization flow and no stable fixed point is found. Consequently, an instability occurs in the paramagnetic region, before one reaches the Curie line, signalling the onset of replica symmetry breaking. [ABSTRACT FROM AUTHOR]

Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular energy levels display multiscaling with the scaling length ℓ = 1/ Mn, where n denotes the number of spins and Mn is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal properties. [ABSTRACT FROM AUTHOR]

The influence of surface defects on the critical properties of magnetic films is studied for Ising models with nearest-neighbour ferromagnetic couplings. The defects include one or two adjacent lines of additional atoms and a step on the surface. For the calculations, both density-matrix renormalization group and Monte Carlo techniques are used. By changing the local couplings at the defects and the film thickness, non-universal features as well as interesting crossover phenomena in the magnetic exponents are observed. [ABSTRACT FROM AUTHOR]

We introduce a model for the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by the landscape itself. By choosing relevant measures of time and potential this self-quenched dynamics can be mapped on to the “True” Self-Avoiding Walk model. This correspondence reveals that the average distance of the walker at time t from its starting point is , where for one dimension and 1/2 for all higher dimensions. Furthermore, the evolution of the landscape is similar to that in growth models with extremal dynamics. [ABSTRACT FROM AUTHOR]