Reconstruction of the finite size canonical ensemble from incomplete micro-canonical data

TL;DR

This paper presents a method to approximate energy distributions and related thermodynamic properties of spin models using incomplete micro-canonical data, demonstrated on the 3-state Potts model.

Contribution

It introduces a novel approach to reconstruct finite size canonical ensembles from partial micro-canonical information, improving estimations of critical properties.

Findings

Accurate estimates of latent heat and critical temperature for the 3-state Potts model.

Demonstrated effectiveness of the method on large cubic lattices up to size 128.

Provided microcanonical property insights relevant for phase transition analysis.

Abstract

In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to eg the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of eg latent heat and critical temperature, as well as the microcanonical properties of interest.