Related papers: Universal Finite-Size-Scaling Functions
We study the four-dimensional Ising spin glass with Gaussian and bond-diluted bimodal distributed interactions via large-scale Monte Carlo simulations and show via an extensive finite-size scaling analysis that four-dimensional Ising spin…
Using single cluster flip Monte Carlo simulations we accurately determine new finite size scaling functions which are expressed only in terms the variable $x = \xi_L / L$, where $\xi_L$ is the correlation length in a finite system of size…
The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that…
The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80\,000 sites. By applying reweighting techniques and finite-size scaling analyses…
Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies…
We study the topology dependence of finite size corrections to the Ising model partition function by considering the model on a triangular lattice embedded on a genus two surface. At criticality we observe a universal shape dependent…
To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process…
Using Finite-Size Scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention in parameterizing the corrections-to-scaling, what is…
For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the reduced free-energy density are calculated by…
We study the probability density function $P(h_m,L)$ of the maximum relative height $h_m$ in a wide class of one-dimensional solid-on-solid models of finite size $L$. For all these lattice models, in the large $L$ limit, a central limit…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
We analyze universal and nonuniversal finite-size effects of lattice systems in a $L^d$ geometry above the upper critical dimension d = 4 within the O(n) symmetric $\phi^4$ lattice theory. On the basis of exact results for $n \to\infty$ and…
We describe a method for approximating the universal scaling functions for the Ising model in a field. By making use of parametric coordinates, the free energy scaling function has a polynomial series everywhere. Its form is taken to be a…
Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high statistics Monte Carlo simulation for several values of the dilution. The results support the…
We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$ universality classes and their finite size dependence using Monte Carlo simulations of improved $\phi^4$ models. Results for the scaling functions are fitted to the…
Based on the results published recently [J. Phys. A: Math. Theor. 50, 065201 (2017)], the universal finite-size contributions to the free energy of the square lattice Ising model on the $L\times M$ rectangle, with open boundary conditions…
We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of…
Systems brought out of equilibrium through a rapid quench from a disordered initial state into an ordered phase undergo physical aging in the form of phase-ordering kinetics, with characteristic dynamical scaling. In many systems, notably…