Crossover scaling in two dimensions

TL;DR

This paper investigates the crossover from Ising-like to classical critical behavior in two-dimensional systems with variable interaction ranges, using a new Monte Carlo method to accurately determine universal scaling functions across the full crossover region.

Contribution

It introduces a novel Monte Carlo approach to accurately analyze the crossover scaling functions in 2D systems with varying interaction ranges, covering the entire critical region.

Findings

Crossover functions are universal across the studied range.

Effective exponents can vary nonmonotonically in the crossover region.

Accurate data obtained for large interaction ranges.

Abstract

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the reduced temperature as well as in the finite-size crossover variable, it has up to now largely evaded a satisfactory numerical determination. Using a new Monte Carlo method, we could obtain accurate results for sufficiently large interactions ranges. Our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal. Also the so-called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region.