A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields

TL;DR

This paper introduces a new scaling relation for critical phenomena involving dangerously irrelevant symmetry-breaking fields, validated through numerical simulations on the 6-state clock model in multiple dimensions.

Contribution

It proposes a novel scaling relation for such fields and demonstrates its validity with numerical evidence, addressing issues with previous order parameter methods.

Findings

The scaling relation holds in 3D and 4D for the 6-state clock model.

Identification of problems with previous order parameter approaches.

Alternative evidence based on mass-dependent fluctuation confirms the relation.

Abstract

We propose a scaling relation for critical phenomena in which a symmetry-breaking field is dengerously irrelevant. We confirm its validity on the 6-state clock model in three and four dimensions by numerical simulation. In doing so, we point out the problem in the previously-used order parameter, and present an alternative evidence based on the mass-dependent fluctuation.