Related papers: Crossover scaling in the two-dimensional three-sta…
The Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a degree (or connectivity) distribution $P(k) \sim k^{-\gamma}$. The ferromagnetic-paramagnetic…
Using $\phi^4$ field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization $M$ for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory…
This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in…
Certain frustrated systems, including spin ice and dimer models, exhibit a Coulomb phase at low temperatures, with power-law correlations and fractionalized monopole excitations. Transitions out of this phase, at which the effective gauge…
We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by…
A model based on microcanonical Monte Carlo method is used to study the application of the temperature gradient along a two-dimensional (2D) Ising system. We estimate the system size effects on thermal conductivity, $K$, for a nano-scale…
Here we consider a one-dimensional $q$-state Potts model with an external magnetic field and an anisotropic interaction that selects neighboring sites that are in the spin state 1. The present model exhibits an unusual behavior in the…
We use Monte Carlo simulations to study the static and dynamical properties of a Potts glass with infinite range Gaussian distributed exchange interactions for a broad range of temperature and system size up to N=2560 spins. The results are…
We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and…
A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram…
By Monte Carlo simulations we study critical properties of the mixed spin-1/2 and spin-1 Ising model on a triangular lattice, considering two different ways of the spin-value distributions on the three sublattices: $(1/2,1/2,1)$ and…
We theoretically investigate the spatial dependence of the order parameter of the two-dimensional semi-infinite Ising model with a free surface at or above the bulk critical temperature. Special attention is paid to the influence of a…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore…
We demonstrate the nontrivial scaling behavior of Ising models defined on (i) a donut-shaped surface and (ii) a curved surface with a constant negative curvature. By performing Monte Carlo simulations, we find that the former model has two…
We carry out Monte Carlo simulations of the three dimensional (3D) lattice London superconductor in zero applied magnetic field, making a detailed finite size scaling analysis of the Meissner transition. We find that the magnetic…
A cluster weight Ising model is proposed by introducing an additional cluster weight in the partition function of the traditional Ising model. It is equivalent to the O($n$) loop model or $n$-component face cubic loop model on the…
Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an…
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the…
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the…