Dimers on surface graphs and spin structures. I

TL;DR

This paper derives a formula linking dimer partition functions on surfaces to discrete spin structures, expanding understanding of their mathematical structure and computation.

Contribution

It introduces a new formula expressing dimer partition function coefficients via discrete spin structures, enhancing theoretical insights.

Findings

Formula for coefficients in terms of discrete spin structures

Connection between dimer models and spin structures

Advancement in mathematical understanding of surface graph dimers

Abstract

Partition functions for dimers on closed oriented surfaces are known to be alternating sums of Pfaffians of Kasteleyn matrices. In this paper, we obtain the formula for the coefficients in terms of discrete spin structures.