Microcanonical entropy for small magnetisations

TL;DR

This paper explores how microcanonical entropy surfaces reveal phase transition features in finite classical spin systems, using symmetry-based Taylor expansions and the four-state vector Potts model as an example.

Contribution

It introduces a symmetry-based Taylor expansion approach to analyze microcanonical entropy and phase transition indicators in finite classical spin systems.

Findings

Microcanonical entropy surfaces exhibit phase transition features in finite systems.

Taylor expansion of entropy explains singular behaviour of order parameters.

Application to the four-state vector Potts model confirms the approach.

Abstract

Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically defined order parameter and susceptibility can be understood from a Taylor expansion of the entropy surface. The general form of the expansion is determined from the symmetry properties of the microcanonical entropy function with respect to the order parameter. The general findings are investigated for the four-state vector Potts model as an example of a classical spin system.