Do crossover functions depend on the shape of the interaction profile?

TL;DR

This study investigates how the shape of interaction profiles influences crossover functions in two-dimensional systems, revealing robustness against profile variations despite the dependence on interaction range.

Contribution

It demonstrates that crossover functions depend on interaction range but are robust to changes in the interaction profile shape in 2D systems.

Findings

Crossover functions depend on the interaction range.

They are robust against variations in the interaction profile shape.

Non-monotonic crossover of susceptibility exponent occurs across different profiles.

Abstract

We examine the crossover from classical to non-classical critical behaviour in two-dimensional systems with a one-component order parameter. Since the degree of universality of the corresponding crossover functions is still subject to debate, we try to induce non-universal effects by adding interactions with a second length scale. Although the crossover functions clearly depend on the range of the interactions, they turn out to be remarkably robust against further variation of the interaction profile. In particular, we find that the earlier observed non-monotonic crossover of the effective susceptibility exponent occurs for several qualitatively different shapes of this profile.