Critical behavior of magnetic thin films as a function of thickness

TL;DR

This study investigates how the critical behavior of magnetic thin films changes with thickness using Monte Carlo simulations of the Ising model, revealing systematic deviations from 2D critical exponents and confirming theoretical predictions.

Contribution

It provides a detailed analysis of the critical exponents' deviations with film thickness and validates the effective exponent concept through Monte Carlo simulations.

Findings

Critical exponents deviate systematically from 2D values with increasing thickness.

The shift in critical temperature agrees with theoretical predictions.

Exponent ν shows small deviation, while β exhibits larger deviation.

Abstract

We study the critical behavior of magnetic thin films as a function of the film thickness. We use the ferromagnetic Ising model with the high-resolution multiple histogram Monte Carlo (MC) simulation. We show that though the 2D behavior remains dominant at small thicknesses, there is a systematic continuous deviation of the critical exponents from their 2D values. We observe that in the same range of varying thickness the deviation of the exponent $\nu$ is rather small, while exponent $\beta$ suffers a larger deviation. We explain these deviations using the concept of "effective" exponents suggested by Capehart and Fisher in a finite-size analysis. The shift of the critical temperature with the film thickness obtained here by MC simulation is in an excellent agreement with their prediction.