Systems with Symmetry Breaking and Restoration

TL;DR

This paper develops a general theoretical framework for systems exhibiting simultaneous symmetry breaking and local symmetry restoration, illustrated through ferroelectric materials with mesoscopic fluctuations, impacting physical properties like sound velocity.

Contribution

It introduces a novel approach based on weighted Hilbert spaces and configuration averaging to describe such complex symmetry phenomena.

Findings

Local symmetry restoration affects sound velocity.

Debye-Waller factor is influenced by symmetry fluctuations.

Framework applicable to various statistical systems with symmetry dynamics.

Abstract

Statistical systems, in which spontaneous symmetry breaking can be accompanied by spontaneous local symmetry restoration, are considered. A general approach to describing such systems is formulated, based on the notion of weighted Hilbert spaces and configuration averaging. The approach is illustrated by the example of a ferroelectric with mesoscopic fluctuations of paraelectric phase. The influence of the local symmetry restoration on the system characteristics, such as sound velocity and Debye-Waller factor, is discussed.