TITLE:
A Cluster Expansion Free Method for Computing Higher Derivatives of the Free Energy and Estimating the Error between the Finite and Infinite Volume Free Energy
AUTHORS:
Assane Lo
KEYWORDS:
Witten Laplacians, Analyticity, Free Energy, Kac-Models
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
31,
2022
ABSTRACT: The theory of phase transitions is one of the branches of statistical physics in which smoothness and continuity play an important role. In fact, phase transitions are characterized mathematically by the degree of non-analyticity of the thermodynamic potentials associated with the given system. In this paper, we propose a method that is not based on cluster expansions for computing the higher derivatives of the free energy and estimating the error between the finite and infinite volume free energy in certain continuum gas models. Our approach is suitable for a direct proof of the analyticity of the pressure or free energy in certain models of Kac-type. The methods known up to now strongly rely on the validity of the cluster expansion. An extension of the method to classical lattice gas models is also discussed.