Computer simulation of the critical behavior of 3D disordered Ising model

TL;DR

This paper uses Monte Carlo simulations to analyze the critical behavior of the 3D disordered Ising model, revealing two universal classes based on disorder strength through finite-size scaling.

Contribution

It introduces a comprehensive numerical study of the disordered Ising model, identifying two distinct universality classes depending on impurity concentration.

Findings

Identification of two universality classes for disordered Ising models

Determination of critical temperatures and exponents across disorder levels

Universal behavior of correlation length and susceptibility near criticality

Abstract

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 length and magnetic susceptibility are determined for samples with various spin concentrations and various linear sizes. The finite-size scaling technique is used for obtaining scaling functions for these quantities, which exhibit a universal behavior in the critical region; the critical temperatures and static critical exponents are also determined using scaling corrections. On the basis of variation of the scaling functions and values of critical exponents upon a change in the concentration, the conclusion is drawn concerning the existence of two universal classes of the critical behavior of the diluted Ising model with different characteristics for weakly and strongly disordered systems.