Phases coexistence and surface tensions for the potts model

Theq states Potts model exhibits a first order phase transition at some inverse temperature β _t between “ordered” and “disordered” phases forq large as proved in 1]. In space dimension 2 we use theduality transformation as aninternal symmetry of the partition function at β _t to derive an estimate on the probability of a contour. This enables us to prove the preceding result and the following new results:

1. The discontinuity of the mass gap at β _t .
2. The existence of astrictly positive surface tension between two ordered phases up to β _t .
3. The existence of a non-zero surface tension between an “ordered” and the “disordered” phase at β _t .