Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models

TL;DR

This study investigates how anisotropy affects finite-size scaling functions in 3D Ising models using Monte Carlo simulations, revealing a transition from two-peak to single-peak structures and unifying 3D and 2D scaling behaviors.

Contribution

The paper provides a detailed analysis of the anisotropy dependence of finite-size scaling functions and offers a unified perspective on 3D and 2D scaling behaviors in anisotropic Ising models.

Findings

Finite-size scaling functions for the magnetization distribution change from two-peak to single-peak with anisotropy variation.

A unified view of 3D and 2D finite-size scaling behaviors is established.

The study demonstrates the impact of anisotropy on critical phenomena in Ising models.

Abstract

The finite-size scaling functions for anisotropic three-dimensional Ising models of size $L_1 \times L_1 \times aL_1$ ($a$: anisotropy parameter) are studied by Monte Carlo simulations. We study the $a$ dependence of finite-size scaling functions of the Binder parameter $g$ and the magnetization distribution function $p(m)$. We have shown that the finite-size scaling functions for $p(m)$ at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing $a$ from 1. We also study the finite-size scaling near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional anisotropy. We have found the three-dimensional and two-dimensional finite-size scaling behavior depending on the parameter which is fixed; a unified view of 3D and 2D finite-size scaling behavior has been obtained for the anisotropic 3D Ising models.