Isometric fluctuation relations for equilibrium states with broken symmetry

TL;DR

This paper derives exact isometric fluctuation relations for equilibrium systems with broken symmetry, applicable to various condensed matter systems, and demonstrates their validity on magnetic and liquid crystal models.

Contribution

The paper introduces a new set of exact fluctuation relations for systems with broken symmetry, extending their applicability to finite-size equilibrium states.

Findings

Relations apply to magnetic systems and nematic liquid crystals.

Validated on Curie-Weiss and XY models.

Implications for spontaneous symmetry breaking.

Abstract

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the $XY$ models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.