Acd. Vanenter et al., COMPLETE ANALYTICITY OF THE 2D POTTS-MODEL ABOVE THE CRITICAL-TEMPERATURE, Communications in Mathematical Physics, 189(2), 1997, pp. 373-393
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.