**Authors: **Zoltan Bajnok, Omar el Deeb, Paul A. Pearce,

**Publish Date**: 2015/04/15

**Volume:** 2015, **Issue:**4, **Pages:** 73-

## Abstract

We consider the non-unitary Lee-Yang minimal model \( \mathrm{\mathcal{M}}\left(2,\;5\right) \) in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels (r, s) = (1, 1), (1, 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of (m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

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