# Finite-size scaling of free energy in the dimer model on a hexagonal domain

## TL;DR

This paper analyzes the finite-size scaling behavior of free energy in the dimer model on a hexagonal lattice, deriving asymptotic expansions and discussing their physical significance and universality.

## Contribution

It provides the first detailed asymptotic expansion of free energy for the dimer model on a hexagonal domain, including various boundary conditions and weight configurations.

## Key findings

- Derived asymptotic expansion of free energy as lattice mesh tends to zero.
- Identified universal features of the free energy expansion coefficients.
- Discussed physical interpretation and universality of the results.

## Abstract

We consider dimer model on a hexagonal lattice. This model can be seen as a "pile of cubes in the box". The energy of configuration is given by the volume of the pile and the partition function is computed by the classical MacMahon formula or, more formally, by the determinant of Kasteleyn matrix. We use the expression for the partition function to derive the scaling behavior of free energy in the limit of lattice mesh tending to zero and temperature tending to infinity. We consider the cases of finite hexagonal domain, of infinite height box and coordinate-dependent Boltzmann weights. We obtain asymptotic expansion of free energy and discuss the universality and physical meaning of the expansion coefficients.