On discrete field theory properties of the dimer and Ising models and their conformal field theory limits

TL;DR

This paper explores the mathematical properties of the Dimer and Ising models on graphs, focusing on partition function formulas and their connections to conformal field theory limits.

Contribution

It provides new gluing formulas for partition function components and partial results linking these models to rational conformal field theories.

Findings

Proved gluing formulas for partition function summands

Obtained partial results on conformal field theory limits

Connected discrete models to fermionic conformal theories

Abstract

We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.