Related papers: Geometric Upper Critical Dimensions of the Ising M…

Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior…

A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…

We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature…

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the…

The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…

We study infinite ``$+$'' or ``$-$'' clusters for an Ising model on an connected, transitive, non-amenable, planar, one-ended graph $G$ with finite vertex degree. If the critical percolation probability $p_c^{site}$ for the i.i.d.~Bernoulli…

Numerical results are presented indicating d_c=4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746-5749…

In this review, we show our results with new interpretation on the critical exponents of thin films obtained by high-performance multi-histogram Monte Carlo simulations. The film thickness $N_z$ consists of a few layers up to a dozen of…

We consider disordered ladders of the transverse-field Ising model and study their critical properties and entanglement entropy for varying width, $w \le 20$, by numerical application of the strong disorder renormalization group method. We…

We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is…

We consider the 3-state Potts model in $d\geq2$ dimensions. For $d$ less than the upper critical dimension $d_\text{crit}$, the model has a critical and a tricritical fixed point. In $d=2$, these fixed points are described by minimal…

We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a…

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic…

We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed…

We consider a random surface representation of the three-dimensional Ising model.The model exhibit scaling behaviour and a new critical index $\k$ which relates $\g_{string}$ for the bosonic string to the exponent $\a$ of the specific heat…

We perform high-statistics Monte Carlo simulations of three-dimensional Ising spin-glass models on cubic lattices of size L: the +- J (Edwards-Anderson) Ising model for two values of the disorder parameter p, p=0.5 and p=0.7 (up to L=28 and…

The gauge glass in dimensions 3 and 4 is studied using a variety of numerical methods, in order to obtain accurate and reliable values for the critical parameters. Detailed comparisons are made of the sensitivity of the different techniques…

This article gives a brief overview on recent advances in experiments of critical exponents in three groups of magnetic materials. Revisiting experimental data verifies that a universality class with the critical exponents beta = 3/8, gamma…

We explore the phase diagram of Ising spins on one-dimensional chains which criss-cross in two perpendicular directions and which are connected by interchain couplings. This system is of interest as a simpler, classical analog of a quantum…