Symmetries of microcanonical entropy surfaces

TL;DR

This paper explores how symmetry properties of the microcanonical entropy surface relate to the invariance group of the Hamiltonian, analyzing their effects on the order parameter and symmetry breaking in different energy regimes.

Contribution

It provides a theoretical framework linking Hamiltonian symmetries to entropy surface properties and investigates symmetry breaking in classical spin systems.

Findings

Symmetry properties of the entropy surface are derived from the Hamiltonian invariance group.

Symmetry breaking occurs in the low energy phase of classical spin systems.

Theoretical results are supported by examples of classical spin systems.

Abstract

Symmetry properties of the microcanonical entropy surface as a function of the energy and the order parameter are deduced from the invariance group of the Hamiltonian of the physical system. The consequences of these symmetries for the microcanonical order parameter in the high energy and in the low energy phases are investigated. In particular the breaking of the symmetry of the microcanonical entropy in the low energy regime is considered. The general statements are corroborated by investigations of various examples of classical spin systems.