The field theory of the q→4+ Potts model

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.