Finite Size Effects at First-Order Phase Transitions Revisited

Abstract

Two years ago a phenomenological theory of finite size scaling at a temperature-driven first order phase transition was proposed by CHALLA et al. [1]. Approximating the energy distribution function by the superposition of two weighted Gaussian functions, the authors found that all finite-size effects, e.g. “rounding” and “shifting” of the transition, depend on the volume of the system L^d, in accordance with previous general scaling arguments. This prediction was successfully tested [1], by carrying out extensive Monte Carlo calculations, on the ten-state (Q=10) Potts model in two dimensions, defined by the Hamiltonian

$$H = - J\mathop \Sigma \limits_{(i,j)} \delta _{\sigma _{\text{i}} \sigma _{\text{j}} } $$

(1)

(where δ is the Kronecker delta, J is the interaction strength, the sum runs over all nearest-neighbor pairs of spins, and σ_j can have Q different values).