Variance of voltages in a lattice Coulomb gas

TL;DR

This paper investigates how the variance of energy differences behaves in a 2D lattice Coulomb gas at high temperatures, using duality with a Gaussian model and symmetry breaking to derive estimates.

Contribution

It introduces a novel analysis of energy variance in lattice Coulomb gases by leveraging duality and symmetry breaking techniques.

Findings

Derived estimates for energy variance differences

Identified the role of symmetry breaking in the Gaussian dual model

Provided insights into high-temperature behavior of Coulomb gases

Abstract

We study the behavior of the variance of the difference of energies for putting an additional electric unit charge at two different locations in the two-dimensional lattice Coulomb gas in the high-temperature regime. For this, we exploit the duality between this model and a discrete Gaussian model. Our estimates follow from a spontaneous symmetry breaking in the latter model.