# Large q expansion of the 2D q-states Potts model

## TL;DR

This paper introduces a recursive method to compute large q expansions of the 2D q-states Potts model free energies, revealing large energy cumulants near the transition for q less than 15.

## Contribution

A new recursive approach based on Fortuin-Kasteleyn representation for calculating large q expansions of the 2D Potts model's free energies.

## Key findings

- Direct computation of ordered phase partition function up to order 10 in 1/√q
- Energy cumulants are large for q around 15 or less
- Predicted specific heats are larger than finite size scaling estimates for q<15

## Abstract

We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn representation of the model. With this procedure, we compute directly the ordered phase partition function up to order 10 in 1/sqrt{q}. The energy cumulants at the transition can be obtained with suitable resummation and come out large for q less or around 15. As a consequence, expansions of the free energies around the transition temperature are useless for not large enough values of q. In particular the pure phase specific heats are predicted to be much larger, at q < 15, than the values extracted from current finite size scaling analysis of extrema, whereas they agree very well with recent values extracted at the transition point.