Electromagnetic Coulomb Gas with Vector Charges and "Elastic'' Potentials : Renormalization Group Equations

TL;DR

This paper derives renormalization group equations for a novel two-dimensional electromagnetic Coulomb gas model with vector charges and elastic interactions, relevant for understanding melting transitions in 2D solids.

Contribution

It introduces a new elastic Coulomb gas model with vector charges and derives its RG equations, extending previous Coulomb gas theories.

Findings

Derived RG equations for the elastic Coulomb gas.

Connected the model to 2D melting transitions.

Highlighted the role of vector charges and elastic potentials.

Abstract

We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges involve both angular couplings and a new electromagnetic potential. This motivates the denomination of ``elastic'' Coulomb gas. Such elastic Coulomb gases arise naturally in the study of the continuous melting transition of two dimensional solids coupled to a substrate, either commensurate or with quenched disorder.