Critical points in coupled Potts models and critical phases in coupled loop models

doi:10.1088/1751-8113/41/21/215001

Critical points in coupled Potts models and critical phases in coupled loop models

Paul Fendley et al 2008 J. Phys. A: Math. Theor. 41 215001 (21pp) doi: 10.1088/1751-8113/41/21/215001

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Paul Fendley^1,2 and Jesper L Jacobsen^3,4
¹ All Souls College and the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
² Department of Physics, University of Virginia, Charlottesville, VA 22904-4714, USA
³ Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
⁴ Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France

Abstract. We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed loop representations. In the continuum limit, the new critical point is described by an SU(2) coset conformal field theory, while in this limit of the critical phase, the two loop models decouple. Using a combination of exact results and numerics, we also obtain the phase diagram in the presence of vacancies. We generalize these results to coupling two Potts models at different Q.

PACS numbers: 05.50.+q, 05.70.Jk

Print publication: Issue 21 (30 May 2008)
Received 19 March 2008
Published 6 May 2008

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Critical points in coupled Potts models and critical phases in coupled loop models

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