The Field Theory of the q->4+ Potts Model

TL;DR

This paper develops an integrable quantum field theory for the q->4+ Potts model, describing its critical behavior and calculating universal amplitude ratios that match numerical and series extrapolations.

Contribution

It constructs the S-matrix and form factors for the massive integrable field theory describing the q->4+ Potts model, providing new analytical insights into its critical properties.

Findings

Universal amplitude ratios agree with Monte Carlo results for q=5.

Correlation length diverges as q approaches 4 from above.

Constructed the exact S-matrix for the associated quantum field theory.

Abstract

The q-state Potts model in two dimensions exhibits a first-order transition for q>4. As q->4+ the correlation length at this transition diverges. We argue that this limit defines a massive integrable quantum field theory whose lowest excitations are kinks connecting 4+1 degenerate ground states. We construct the S-matrix of this theory and the two-particle form factors, and hence estimate a number of universal amplitude ratios. These are in very good agreement with the results of extrapolated series in q^(-1/2) as well as Monte Carlo results for q=5.