Boundary Critical Phenomena in the Three-State Potts Model

TL;DR

This work analyzes boundary critical phenomena in the two-dimensional three-state Potts model through boundary conformal field theory, duality, and renormalization-group methods. By combining fusion with nonbulk Virasoro primaries and an orbifold construction, the authors demonstrate a nearly complete boundary-state set that includes a novel boundary condition, beyond the previously known free, fixed, and mixed states. The new boundary condition is shown to be dual to the mixed one, and the quantum Potts chain reveals a rich phase diagram with duality- and RG-driven flows linking the different boundary fixed points. The results illuminate the role of nonbulk operators in boundary criticality and connect to impurity problems such as Kondo physics, while respecting the g-theorem in the boundary context.

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.

Figures (3)

• Figure 1: Schematic phase diagram of the quantum chain version of the Potts model with a complex boundary transverse field. Arrows indicate direction of RG flows as the energy scale is decreased.
• Figure 2: Site, link and dual lattice variables.
• Figure 3: Boundary variables.