Excited Boundary TBA in the Tricritical Ising Model

TL;DR

This paper derives excited state boundary TBA equations for the tricritical Ising model, describing boundary RG flows induced by a perturbing boundary field, using integrable lattice models and their continuum limit.

Contribution

It introduces a novel derivation of boundary TBA equations for excited states in the tricritical Ising model, linking lattice models to boundary RG flows.

Findings

Derived boundary TBA equations for excited states.

Mapped boundary RG flows between fixed points.

Connected transfer matrix zeros to Virasoro character transformations.

Abstract

By considering the continuum scaling limit of the $A_{4}$ RSOS lattice model of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state TBA equations describing the boundary flows of the tricritical Ising model. Fixing the bulk weights to their critical values, the integrable boundary weights admit a parameter $\xi $ which plays the role of the perturbing boundary field $\phi_{1,3}$ and induces the renormalization group flow between boundary fixed points. The boundary TBA equations determining the RG flows are derived in the $\mathcal{B}_{(1,2)}\to \mathcal{B}_{(2,1)}$ example. The induced map between distinct Virasoro characters of the theory are specified in terms of distribution of zeros of the double row transfer matrix.