On the large order behaviour of the Potts model

TL;DR

This paper generalizes a technique for analyzing the large order behavior of the Potts model's perturbative expansion, establishing an equivalence with a bosonic field theory for all n and deriving explicit expressions.

Contribution

It extends previous work by providing a general method for all n, linking the Potts model to bosonic field theory, and deriving explicit large order behavior expressions.

Findings

Derived explicit large order behavior expressions in terms of n.

Established equivalence with bosonic field theory for all n.

Generalized previous techniques to all n in the Potts model.

Abstract

Following the work by Houghton, Reeve and Wallace about an alternative formulation of the $n \to 0 $ limit of the $(n+1)$ state Potts model in field theory for the large order behaviour of the perturbative expansion, we generalise their technique to all $n$ by establishing an equivalence in perturbation theory order by order with another bosonic field theory. Restricting ourselves to a cubic interaction, we obtain an explicit expression (in terms of~$n$) for the large order behaviour of the partition function.