We study the finite-size effects at a temperature-driven first-order transition by analyzing various moments of the energy distribution. The distribution function for the energy is approximated by the superposition of two weighted Gaussian functions yielding quantitative estimates for various quantities and scaling form for the specific heat. The rounding of the singularities and the shifts in the location of the specific-heat maximum are analyzed and the characteristic features of a first-order transition are identified. The predictions are tested on the ten-state Potts model in two dimensions by carrying out extensive Monte Carlo calculations. The results are found to be in good agreement with theory. Comparison is made with the second-order transitions in the two- and three-state Potts models.
Challa et al. (1986) studied this question.