Shape dependence of the finite-size scaling limit in a strongly anisotropic $O(\infty)$ model

TL;DR

This paper investigates how the shape of a system influences the finite-size scaling behavior in a strongly anisotropic O(N) model at large N, revealing that scaling can appear with incorrect anisotropy exponents, which may be effective rather than true critical exponents.

Contribution

It demonstrates that finite-size scaling can be observed even with incorrect anisotropy exponents, highlighting the importance of shape dependence in anisotropic systems.

Findings

Scaling observed despite incorrect anisotropy exponent

Effective exponents may differ from true critical exponents

Implications for numerical studies of anisotropic systems

Abstract

We discuss the shape dependence of the finite-size scaling limit in a strongly anisotropic O(N) model in the large-N limit. We show that scaling is observed even if an incorrect value for the anisotropy exponent is considered. However, the related exponents may only be effective ones, differing from the correct critical exponents of the model. We discuss the implications of our results for numerical finite-size scaling studies of strongly anisotropic systems.