Eur. Phys. J. B 64, 307-314 (2008)
https://doi.org/10.1140/epjb/e2008-00109-x

Monte Carlo methods for the study of phase transitions and phase equilibria

Institut of Physics, Johannes Gutenberg University, 55099 Mainz, Germany

Corresponding author: ^a kurt.binder@uni-mainz.de

Received: 11 October 2007
Revised: 28 January 2008
Published online: 12 March 2008

Abstract

Monte Carlo methods can predict macroscopic properties of N-body systems from the (classical) Hamiltonian describing the interactions between the particles and hence can serve as a basic tool of equilibrium statistical mechanics, avoiding uncontrolled approximations. However, a necessary ingredient is the control of finite size effects. For this purpose, the finite size scaling analysis of suitable distribution functions is a powerful tool. The basic ideas of this approach will be discussed, including extensions to critical phenomena where the hyperscaling relation between critical exponents is violated (colloid-polymer mixtures in random media as a realization of the random field Ising model, phase transitions caused by competition of interfacial and surface effects, etc.) Finite size effects on two-phase coexistence cause the existence of a van-der-Waals-like loop, but it has a completely different origin, the “spinodal” reflecting the “droplet evaporation/condensation” transition. Also the possibility to extract interface free energies is discussed.