Dimer Model: Full Asymptotic Expansion of the Partition Function

TL;DR

This paper rigorously derives the complete asymptotic expansion of the dimer model's partition function on a square lattice torus, accounting for general weights and lattice dimensions, and clarifies the dependence on lattice parity.

Contribution

It provides a rigorous proof of the full asymptotic expansion of the dimer model's partition function, extending previous results and estimating error terms precisely.

Findings

Asymptotic expansion depends on the parity of n

Error term in the expansion is rigorously estimated

Results generalize previous asymptotic analyses

Abstract

We give a complete rigorous proof of the full asymptotic expansion of the partition function of the dimer model on a square lattice on a torus for general weights $z_h, z_v$ of the dimer model and arbitrary dimensions of the lattice $m, n$. We assume that $m$ is even and we show that the asymptotic expansion depends on the parity of $n$. We review and extend the results of Ivashkevich, Izmailian, and Hu [6] on the full asymptotic expansion of the partition function of the dimer model, and we give a rigorous estimate of the error term in the asymptotic expansion of the partition function.