Quantum Symmetry on Potts Model

TL;DR

This paper explores how quantum group symmetry in the Potts model varies with parameters, revealing that small changes can cause significant shifts in symmetry groups, indicating phase transitions.

Contribution

It introduces the concept of quantum group symmetry in the Potts model and demonstrates how slight parameter variations can lead to drastic symmetry changes.

Findings

Quantum symmetry groups can change abruptly with model parameters.

Classical symmetry may remain unchanged despite quantum symmetry shifts.

Parameter variations can signal phase transitions.

Abstract

We formulate the notion of quantum group symmetry of the Hamiltonian corresponding to Potts model and compute it for few simple models. Our examples illustrate how a slight change of the model parameter may result in a drastic change of the quantum symmetry group, (in some cases, the classical symmetry group remains unaffected) signifying a case of phase transition.