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Lattice Realization of Complex Conformal Field Theories: Two-Dimensional Potts Model with Q>4 States
Jesper Lykke Jacobsen1,2,3, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique de l'Ecole Normale Supérieure, PSL Research University, <a href="https://ror.org/02en5vm52">Sorbonne Université</a>, Université Paris Cité, 24 rue Lhomond, 75005 Paris, France.
Abstract:
The two-dimensional Q-state Potts model with real couplings has a first-order transition for Q>4. We study a loop-model realization in which Q is a continuous parameter. This model allows for the collision of a critical and a tricritical fixed point at Q=4, which then emerge as complex conformally invariant theories at Q>4, or even complex Q, for suitable complex coupling constants. All critical exponents can be obtained as analytic continuation of known exact results for Q≤4. We verify this scenario in detail for Q=5 using transfer-matrix computations.
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