VERY LARGE ENERGY CUMULANTS OF THE 2D POTTS-MODEL

The energy cumulants of the 2d q-states Potts model are obtained from a large q expansion of its partition function up to order 10 in 1/root q. The numerical values of these cumulants at the transition, as given by Pade resummation, are very large for q less than or similar to 15. For example at q = 10 we found F-(2) similar to 10, F-(3) similar to 2 10(3), F-(4) similar to 10(6), F-(5) similar to 10(9), F-(6) similar to 10(12). As a consequence the standard finite size analysis away from the transition point is only possible for very large lattices and the description of energy probability distributions with 2 gaussian peaks is inadequate.