Lattice Realization of Complex Conformal Field Theories: Two-Dimensional Potts Model with Q > 4 States 1

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.