Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

TL;DR

This paper analyzes the integrable structure of q-state Potts models near criticality, closing the bootstrap for certain regimes and revealing connections to algebraic structures like Freudenthal's magic square.

Contribution

It demonstrates the bootstrap closure for scaling q-state Potts models near critical and tricritical points, extending previous S-matrix proposals and uncovering algebraic links.

Findings

Bootstrap closure achieved for all critical points

Bootstrap closure for tricritical points when 4>q>=2

Connection to Freudenthal's magic square

Abstract

We discuss the q-state Potts models for q<=4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4>q>=2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models.