Dimers and the Ising model

TL;DR

This paper establishes a novel connection between the ground states of the Ising model and dimer coverings, providing new insights and methods for constructing and analyzing highly degenerate ground state models.

Contribution

It introduces a new relationship linking Ising model ground states with dimer coverings, enabling the construction of such models and deriving the dimer generating function from the Ising free energy.

Findings

Derived the generating function for dimers from the Ising model free energy

Provided a method to construct Ising models with highly degenerate ground states

Revealed a new perspective on the relationship between Ising models and dimer coverings

Abstract

We present a innovative relationship between ground states of the Ising model and dimer coverings which sheds new light on the Ising Models with highly degenerated ground states and enables one to construct such models. Thanks to this relationship we also find the generating function for dimers as the appropriate limit of the free energy per spin for the Ising model.