Series expansions without diagrams

TL;DR

The paper presents a recursive enumeration method to generate low and high temperature series expansions for discrete statistical models, offering a competitive alternative to diagrammatic techniques.

Contribution

It introduces a recursive enumeration scheme applicable to any discrete model, demonstrated on the Ising model and adaptable to Potts models.

Findings

Generated low temperature series in up to five dimensions

Produced high temperature series in three dimensions

Method is competitive with diagrammatic approaches

Abstract

We discuss the use of recursive enumeration schemes to obtain low and high temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagramatic approaches and is easily generalizable. We illustrate the approach using the Ising model and generate low temperature series in up to five dimensions and high temperature series in three dimensions. The method is general and can be applied to any discrete model. We describe how it would work for Potts models.