Critical properties of the spherical model in the microcanonical formalism

TL;DR

This paper demonstrates the equivalence of microcanonical and canonical ensembles in the spherical model, showing that critical properties are consistent across both approaches, thus validating microcanonical analysis for phase transitions.

Contribution

It explicitly calculates and compares the critical properties of the spherical model in the microcanonical ensemble with canonical results, confirming ensemble equivalence.

Findings

Microcanonical and canonical ensembles yield identical critical properties for the spherical model.

Ensemble equivalence holds for systems with short-range interactions undergoing continuous phase transitions.

Microcanonical approach can reliably be used to study phase transitions in such systems.

Abstract

Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence holds for systems that undergo a continuous phase transition in the infinite volume limit so that the properties of the transition can also be investigated in the microcanonical approach. Considering as example the spherical model the ensemble equivalence is explicitly demonstrated by calculating the critical properties in the microcanonical ensemble and comparing them to the well-known canonical results.