Mangetic properties of Ising thin-films with cubic lattices

TL;DR

This study uses Monte Carlo simulations and mean-field calculations to analyze the magnetic properties and critical behavior of Ising thin-films with cubic lattices, revealing a dimensional crossover and universality in critical exponents.

Contribution

It introduces an extension of finite size scaling theory for thin films and compares Monte Carlo results with mean-field calculations to understand dimensional crossover effects.

Findings

Magnetic behavior transitions from 2D to 3D with increasing film thickness.

Critical temperature approaches bulk value as thickness increases.

Critical exponents remain close to 2D universality for up to eight layers.

Abstract

We have used Monte Carlo simulations to observe the magnetic behaviour of Ising thin-films with cubic lattice structures as a function of temperature and thickness especially in the critical region. The fourth order Binder cumulant is used to extract critical temperatures, and an extension of finite size scaling theory for reduced geometry is derived to calculate the critical exponents. Magnetisation and magnetic susceptibility per spin in each layer are also investigated. In addition, mean-field calculations are also performed for comparison. We find that the magnetic behaviour changes from two dimensional to three dimensional character with increasing thickness of the film. The crossover of the critical temperature from a two dimensional to a bulk value is also observed with both the Monte Carlo simulations and the mean-field analysis. Nevertheless, the simulations have shown that the critical exponents only vary a little from their two dimensional values. In particular, the results for films with up to eight layers provide a strong indication of two dimensional universality.