Interacting Fermions Picture for Dimer Models

TL;DR

This paper introduces the Interacting Fermions Picture as a novel theoretical framework for classical dimer models, improving upon Coulomb Gas methods and explaining both weak and strong interaction behaviors.

Contribution

It proposes a new fermionic representation for dimer models that overcomes limitations of previous Coulomb Gas approaches and clarifies interaction effects.

Findings

The Interacting Fermions Picture better matches numerical results.

Peierls' argument explains strong interaction behavior.

The new approach simplifies the theoretical understanding of dimer models.

Abstract

Recent numerical results on classical dimers with weak aligning interactions have been theoretically justified via a Coulomb Gas representation of the height random variable. Here we propose a completely different representation, the Interacting Fermions Picture, which avoids some difficulties of the Coulomb Gas approach and provides a better account of the numerical findings. Besides, we observe that Peierls' argument explains the behavior of the system in the strong interaction case.