LARGE ENERGY CUMULANTS IN THE 2D POTTS-MODEL AND THEIR EFFECTS IN FINITE-SIZE ANALYSIS

We develop an ansatz for expressing the free energy of the two-dimensi onal q-states Potts model for q > 4 near its first order phase transit ion point. We notice that for the moderate values of q less than or si milar to 15, the energy profile at the phase transition is not express ible as a sum of gaussians. We discuss how this affects the traditiona l finite size analysis of this phase transition. In particular, the do minant length scale governing the finite size corrections turns out to be much (similar to 6 times) larger than the largest correlation leng th in the problem.