Nonuniversal finite-size scaling in anisotropic systems

TL;DR

This paper investigates how anisotropic interactions in certain physical systems lead to nonuniversal behavior in finite-size scaling, showing that isotropy cannot be restored through simple transformations.

Contribution

It demonstrates that anisotropic systems with non-cubic symmetry exhibit nonuniversal finite-size scaling and bulk correlation functions, challenging the idea of universality in such contexts.

Findings

Two-scale factor universality is absent in bulk correlation functions.

Finite-size scaling functions are nonuniversal in anisotropic systems.

Isotropy cannot be restored by anisotropic scale transformations in confined systems.

Abstract

We study the bulk and finite-size critical behavior of the O$(n)$ symmetric $\phi^4$ theory with spatially anisotropic interactions of non-cubic symmetry in $d<4$ dimensions. In such systems of a given $(d,n)$ universality class, two-scale factor universality is absent in bulk correlation functions, and finite-size scaling functions including the Privman-Fisher scaling form of the free energy, the Binder cumulant ratio and the Casimir amplitude are shown to be nonuniversal. In particular it is shown that, for anisotropic confined systems, isotropy cannot be restored by an anisotropic scale transformation.