Finite-volume spectra of the Lee-Yang model

Open Access
Regular Article - Theoretical Physics

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.

Keywords

Lattice Integrable Models Field Theories in Lower Dimensions Lattice Quantum Field Theory Integrable Field Theories 

Notes

Open Access

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Zoltan Bajnok
    • 1
  • Omar el Deeb
    • 1
    • 2
  • Paul A. Pearce
    • 3
  1. 1.MTA Lendület Holographic QFT GroupWigner Research Centre for PhysicsBudapest 114Hungary
  2. 2.Physics Department, Faculty of ScienceBeirut Arab University (BAU)BeirutLebanon
  3. 3.School of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia

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