Related papers: Universality and logarithmic corrections in two-di…
The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size…
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…
We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…
A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic…
Monte Carlo results for the moments <M^k> of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary…
We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation…
Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with $S=1/2$ and $S=1$ are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in…
We briefly review the Ising model with uncorrelated, quenched random-site or random-bond disorder, which has been controversial in both two and four dimensions. In these dimensions, the leading exponent alpha, which characterizes the…
We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…
We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each…
The critical behavior of the disordered ferromagnetic Ising model is studied numerically by the Monte Carlo method in a wide range of variation of concentration of nonmagnetic impurity atoms. The temperature dependences of correlation…
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…
We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of…
In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a…
We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with $N$ nodes and $N^{\gamma}$ edges, with $1 < \gamma \leq 2$. By conveniently rescaling the coupling constant, the free…
It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties. However, no mathematical proof of universality and conformal…
Universality classes encompass the analogous thermodynamic behavior of unlike physical systems, at different spatial dimensions $d$, in the vicinity of their critical point. Critical exponents define these classes, with the Ising model…
Using the bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangle, rhombus, trapezoid, hexagon and rectangle. The…