Dimer model on the square lattice with interface

TL;DR

This paper analyzes the dimer model on an infinite square lattice with an interface, deriving exact formulas for the inverse Kasteleyn operator and studying its asymptotic behavior to understand local statistics.

Contribution

It provides an exact integral form of the inverse Kasteleyn operator for the dimer model with interface and analyzes its asymptotics across different lattice regions.

Findings

Derived exact integral form of the inverse Kasteleyn operator

Analyzed asymptotic behavior in various lattice regions

Gained insights into local statistics of the dimer model

Abstract

In this exposition, we consider the dimer problem on an infinite square lattice with partially non-periodic edge weights, which we refer to as the square lattice with interface. In particular, we compute an exact integral form of the inverse Kasteleyn operator and study its asymptotics behavior in different regions of the lattice to gain a general understanding of the local statistics of the model.