Enumeration of the self-avoiding polygons on a lattice by the Schwinger-Dyson equations

TL;DR

This paper introduces a method to compute the generating function of self-avoiding polygons on a lattice using Schwinger-Dyson equations from statistical mechanics, providing a novel analytical approach.

Contribution

It presents a new analytical technique linking Schwinger-Dyson equations to enumeration of self-avoiding polygons on lattices.

Findings

Derivation of generating functions for self-avoiding polygons

Application of Schwinger-Dyson equations to lattice models

Potential for exact enumeration methods

Abstract

We show how to compute the generating function of the self-avoiding polygons on a lattice by using the statistical mechanics Schwinger-Dyson equations for the correlation functions of the $N$-vector spin model on that lattice.