Dimer Model: Full Asymptotic Expansion of the Partition Function

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.

26 pages, 1 figure

References in corpus (1)

• The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice

Cited by in corpus (4)

• Exact finite-size corrections in the dimer model on a planar square lattice
• Discrete and zeta-regularized determinants of the Laplacian on polygonal domains with Dirichlet boundary conditions
• Exact finite-size corrections in the dimer model on a cylinder
• The boundary disorder correlation for the Ising model on a cylinder