Conformal boundary conditions in the critical O(n) model and dilute loop models

TL;DR

This paper analyzes the conformal boundary conditions of the two-dimensional dilute O(n) model, identifying dual solutions, boundary operators, and phase flows, and relates these to open boundary conditions and crossing probabilities.

Contribution

It introduces dual solutions to boundary Yang-Baxter equations for the dilute O(n) model and characterizes boundary critical points and their flows.

Findings

Identified dual boundary solutions describing anisotropic transitions

Computed boundary state entropies and phase diagram

Derived new crossing probabilities for Ising domain walls

Abstract

We study the conformal boundary conditions of the dilute O(n) model in two dimensions. A pair of mutually dual solutions to the boundary Yang-Baxter equations are found. They describe anisotropic special transitions, and can be interpreted in terms of symmetry breaking interactions in the O(n) model. We identify the corresponding boundary condition changing operators, Virasoro characters, and conformally invariant partition functions. We compute the entropies of the conformal boundary states, and organize the flows between the various boundary critical points in a consistent phase diagram. The operators responsible for the various flows are identified. Finally, we discuss the relation to open boundary conditions in the O(n) model, and present new crossing probabilities for Ising domain walls.