Boundary Critical Phenomena in the Three-State Potts Model

TL;DR

This paper investigates boundary critical phenomena in the 2D three-state Potts model using conformal field theory, revealing a complete set of boundary conditions including a newly identified one, and explores their dualities and phase diagram.

Contribution

It introduces a comprehensive set of boundary conditions for the 3-state Potts model, including a novel boundary condition obtained through fusion and orbifold methods.

Findings

Discovered a new boundary condition in the 3-state Potts model.

Demonstrated duality between the new boundary condition and the mixed boundary conditions.

Analyzed the phase diagram of the quantum chain version using duality and renormalization group.

Abstract

Boundary critical phenomena are studied in the 3- State Potts model in 2 dimensions using conformal field theory, duality and renormalization group methods. A presumably complete set of boundary conditions is obtained using both fusion and orbifold methods. Besides the previously known free, fixed and mixed boundary conditions a new one is obtained. This illustrates the necessity of considering fusion with operators that don't occur in the bulk spectrum, to obtain all boundary conditions. It is shown that this new boundary condition is dual to the mixed ones. The phase diagram for the quantum chain version of the Potts model is analyzed using duality and renormalization group arguments.