LARGE Q EXPANSION OF THE 2D Q-STATES POTTS-MODEL

We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn r epresentation of the model. With this procedure, we compute directly t he ordered phase partition function up to order 10 in 1/root q. The en ergy cumulants at the transition can be obtained with suitable resumma tion and come out large for q less than or similar to 15. The size of these cumulants has important implications for finite size scaling pre dictions, explaining in particular recent discrepancies between the va lues for the pure phase specific heats obtained from current finite si ze scaling analysis of extrema and those obtained at the transition po int by different methods.