Excited TBA equations I: Massive tricritical Ising model

Paul A. Pearce, Leung Chim, Changrim Ahn

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We consider the massive tricritical Ising model M(4,5) perturbed by the thermal operator φ1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massive thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A4 lattice model of Andrews, Baxter and Forrester (ABF) in Regime III. The complete classification of excitations, in terms of (m,n) systems, is precisely the same as at the conformal tricritical point. Our methods also apply on a torus but we first consider (r,s) boundaries on the cylinder because the classification of states is simply related to fermionic representations of single Virasoro characters χr,s(q). We study the TBA equations analytically and numerically to determine the conformal UV and free particle IR spectra and the connecting massive flows. The TBA equations in Regime IV and massless RG flows are studied in Part II.

Original languageEnglish
Pages (from-to)539-568
Number of pages30
JournalNuclear Physics, Section B
Issue number3
StatePublished - 14 May 2001

Bibliographical note

Funding Information:
PAP is supported by the Australian Research Council and thanks the Asia Pacific Center for Theoretical Physics for support to visit Seoul. CA is supported in part by KOSEF 1999-2-112-001-5, MOST-99-N6-01-01-A-5 and thanks Melbourne University for hospitality. PAP and CA thank Francesco Ravanini for hospitality at Bologna University where part of this work was also carried out. We also thank David O'Brien and Peter Bouwknegt for assistence.


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