Fluctuation relations for equilibrium states with broken discrete or continuous symmetries

TL;DR

This paper derives isometric fluctuation relations for equilibrium systems with broken symmetries, revealing how probability ratios of opposite fluctuations depend exponentially on external fields and applied to various magnetic and liquid crystal models.

Contribution

It introduces new fluctuation relations for equilibrium broken-symmetry states, extending concepts from non-equilibrium physics and applying them to diverse models including quantum systems.

Findings

Relations hold for models with discrete and continuous symmetries.

Explicit calculations for magnetic and liquid crystal models.

Extension to quantum systems demonstrated.

Abstract

Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues obtained for non-equilibrium systems where the broken symmetry is time reversal. At equilibrium, these relations show that the ratio of the probabilities of opposite fluctuations goes exponentially with the symmetry-breaking external field and the magnitude of the fluctuations. These relations are applied to the Curie-Weiss, Heisenberg, and $XY$~models of magnetism where the continuous rotational symmetry is broken, as well as to the $q$-state Potts model and the $p$-state clock model where discrete symmetries are broken. Broken symmetries are also considered in the anisotropic Curie-Weiss model. For infinite systems, the results are calculated using large-deviation theory. The relations are also applied to mean-field models of nematic liquid crystals where the order parameter is tensorial. Moreover, their extension to quantum systems is also deduced.