Fused Potts Models

TL;DR

This paper introduces a family of fused Potts models linked to quantum spin chains, analyzing their interactions, symmetries, phase diagrams, and critical behaviors, extending known results to more complex multi-spin interactions.

Contribution

It develops a general framework for fused Potts models related to higher spin quantum chains, including detailed examples and phase diagram analysis, extending Baxter's and Affleck's methods.

Findings

Computed spontaneous magnetizations for Q>4 on the phase transition line

Mapped the full phase diagram for spin one ($k=2$) models

Identified critical lines and massless phases in the models

Abstract

Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin chain. These Potts model have still variables taking values $1,\ldots,Q$ ($\sqrt{Q}=q+q^{-1}$) but they have a set of complicated multi spin interactions. The general technique to compute these interactions, the resulting lattice geometry, symmetries, and the detailed examples of $k=2,3$ are given. For $Q>4$ spontaneous magnetizations are computed on the integrable first order phase transition line, generalizing Baxter's results for $k=1$. For $Q\leq 4$, we discuss the full phase diagram of the spin one ($k=2$) anisotropic and ${\rm U}_{q}{\rm su}(2)$ invariant quantum spin chain (it reduces in the limit $Q=4$ ($q=1$) to the much studied phase diagram of the isotropic spin one quantum chain). Several critical lines and massless phases are exhibited. The appropriate generalization of the Valence Bond State method of Affleck et al. is worked out.