MONTE-CARLO STUDIES OF FINITE-SIZE EFFECTS AT 1ST-ORDER TRANSITIONS

First-order phase transitions are ubiquitous in nature but their presence is often uncertain because of the effects which finite size has on all transitions. In this article we consider a general treatment of size effects on lattice systems with discrete degrees of freedom and which undergo a first-order transition in the thermodynamic limit. We review recent work involving studies of the distribution functions of the magnetization and energy at a first-order transition in a finite sample of size N connected to a bath of size N’. Two cases: N = ∞ and N = finite are considered. In the former (canonical ensemble) case, the distributions are approximated by a superposition of Gaussians corresponding to the different phases; all finite-size effects then vary as N or 1/N. The latter case involves the Gaussian ensemble where the entropy of the bath has a convenient form; for small N, first-order transitions are characterized by van der Waals loops in (for example) the energy vs. temperature curves. Results from extensive Monte Carlo simulations of Islng and Potts models in d = 2 are presented to confirm the predictions. Comparison is made with data from second-order transitions to show that the order of a transition can be distinguished through such studies, although problems still occur for first-order transitions very close to critical points. © 1990, Taylor & Francis Group, LLC. All rights reserved.