FINITE-SIZE SCALING AND MONTE-CARLO SIMULATIONS OF 1ST-ORDER PHASE-TRANSITIONS

We develop a detailed finite-size-scaling theory at a general, asymmetric, temperature-driven, strongly first-order phase transition in a system with periodic boundary conditions. We compute scaling functions for various cumulants of energy in the form U(L,t) = U0(tL(d)) + L(-d)U1(tL(d)) with t = 1 - T(c)/T. In particular, we consider the specific heat and Binder's fourth cumulant and show this has a minimum value of 2/3 - (e1/e2-e2/e1)2/12 + O(L(-d)) at a temperature T(c)(2)(L) - T(c) = O(L(-d)). Various other pseudocritical temperatures corresponding to extrema of other cumulants are evaluated. We compare these theoretical predictions with extensive Monte Carlo simulations of the nominally strong first-order transitions in the eight- and ten-state Potts models in two dimensions for system sizes L less-than-or-equal-to 50. The ten-state simulations agree with theory in all details in contrast to the eight-state data, and we give estimates for the bulk specific heats at T(c) using all exactly known analytic results. A criterion is developed to estimate numerically whether or not system sizes used in a simulation of a first-order transition are in the finite-size-scaling regime.