Excited TBA equations II: Massless flow from tricritical to critical Ising model

Paul A. Pearce, Leung Chim, Changrim Ahn

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We consider the massless tricritical Ising model M(4,5) perturbed by the thermal operator 1,3 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 massless 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 IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.

Original languageEnglish
Pages (from-to)579-606
Number of pages28
JournalNuclear Physics, Section B
Issue number3
StatePublished - 30 Jun 2003

Bibliographical note

Funding Information:
P.A.P. is supported by the Australian Research Council and thanks the Asia Pacific Center for Theoretical Physics for support to visit Seoul. C.A. is supported in part by Korea Research Foundation 2002-070-C00025, KOSEF 1999-00018. We thank Giuseppe Mussardo for discussions.


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