Boundary CFT and tensor network approach to surface critical phenomena of the tricritical 3-state Potts model

TL;DR

This paper investigates the surface critical phenomena of the tricritical 3-state Potts model using boundary conformal field theory and tensor network methods, classifying boundary conditions and mapping fixed points.

Contribution

It provides a detailed classification of boundary fixed points in the tricritical 3-state Potts BCFT and numerically realizes most of them on the lattice.

Findings

Identified 11 boundary fixed points realizable on the lattice.

Mapped the surface phase diagram using tensor network renormalization.

Discovered the last fixed point is outside the physical parameter space.

Abstract

One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works [Y. Deng and H. W. J. Bl\"ote, Phys. Rev. E 70, 035107(R) (2004); Phys. Rev. E 71, 026109 (2005)], we analyze it from the viewpoint of the boundary conformal field theory (BCFT). The complete classification of the conformal boundary conditions for the minimal BCFTs discussed in [R. E. Behrend et al., Nucl. Phys. B 579, 707 (2000)] allows us to collect the twelve boundary fixed points in the tricritical 3-state Potts BCFT. Employing the tensor network renormalization method, we numerically study the surface phase diagram of the tricritical 3-state Potts model in detail, and reveal that the eleven boundary fixed points among the twelve can be realized on the lattice by controlling the external field and coupling strength at the boundary. The last unfound fixed point would be out of the physically sound region in the parameter space, similarly to the `new' boundary condition in the 3-state Potts BCFT.