COMPLETE ANALYTICITY OF THE 2D POTTS-MODEL ABOVE THE CRITICAL-TEMPERATURE

We investigate the complete analyticity (CA) of the two-dimensional q- state Potts model for large values of q, We are able to prove it for e very temperature T > T-cr(q), provided we restrict ourselves to nice s ubsets, their niceness depending on the temperature T. Contrary to thi s restricted complete analyticity (:RCA), the full CA is known to fail for some values of the temperature above T-cr(q). Our proof is based on Pirogov-Sinai theory and cluster expansions for the Fortuin-Kastele yn representation, which are available for the Potts model at all temp eratures, provided q is large enough.