Free energy analyticity of the disordered XY model and Debye screening in the 2D Coulomb gas

TL;DR

This paper proves the analyticity of free energy in disordered regimes for the XY model, Coulomb gas, and square well model, and establishes strong Debye screening in the Coulomb gas.

Contribution

It introduces new proofs of free energy analyticity and Gibbs measure properties for these models, including a strong Debye screening result.

Findings

Free energy is analytic in the disordered regime for all three models.

Gibbs measures are factors of i.i.d. with exponentially decaying information clusters.

Strong Debye screening holds with arbitrary local observables in the Coulomb gas.

Abstract

We consider three models of statistical mechanics: the classical XY model in arbitrary dimension, the lattice Coulomb gas in dimension two, and the square well model in arbitrary dimension. For each of these three models, we prove that the free energy is analytic in the disordered regime (the square well model is disordered at any positive temperature). In order to prove these results, we prove that the Gibbs measures of these models are factors of i.i.d. with information clusters of exponentially decaying size (volume). In the case of the Coulomb gas, we obtain a strong version of Debye screening with an arbitrary number of arbitrary local observables of the Coulomb gas, and we prove that the Debye phase contains the complement of the Berezinskii-Kosterlitz-Thouless phase.