On the large order behaviour of 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.