Lattice Realization of Complex Conformal Field Theories: Two-Dimensional Potts Model with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Q</mml:mi> <mml:mo>></mml:mo> <mml:mn>4</mml:mn> </mml:math> States
Jesper Lykke Jacobsen, Kay Jörg Wiese
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.
Topics & Concepts
Conformal mapLattice (music)Potts modelPhysicsMathematical physicsStatistical physicsIsing modelMathematicsGeometryAcousticsPhysics of Superconductivity and MagnetismQuantum many-body systemsTheoretical and Computational Physics