Tunneling and the spectrum of the Potts model

The three-dimensional, three-state Potts model is studied as a paradigm for high-temperature quantum chromodynamics. In a high-statistics numerical simulation using a Swendson-Wang algorithm, we study cubic lattices of dimension as larger as 643 and measure correlation functions on long lattices of dimension 202 x 120 and 302 x120. These correlations are controlled by the spectrum of the transfer matrix. the spectrum is studied in the vicinity of the phase transition. The analysis classifies the spectral levels according to an underlying S3 symmetry. Near the phase transition the spectrum agrees nicely with a simple four-component Hamiltonian model. In the context of this model, we find that low-temperature ordered-ordered interfaces nearly always involve a disordered phase intermediate. We use a spectral method for determining the surface tension between phases.