Order parameter conditions from mutual information and symmetry conditions

TL;DR

This paper enhances the mutual information method for determining order parameters in systems with many degenerate vacuums by incorporating symmetry-based constraints, reducing arbitrariness in the definitions.

Contribution

It introduces symmetry-based constraints to improve the mutual information method for complex systems with multiple degenerate vacuums.

Findings

Reduced arbitrariness in order parameter definitions

Enhanced method for systems with many degenerate vacuums

Better constraints for symmetry-breaking scenarios

Abstract

The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.