Journal
EUROPEAN PHYSICAL JOURNAL B
Volume 64, Issue 3-4, Pages 307-314Publisher
SPRINGER
DOI: 10.1140/epjb/e2008-00109-x
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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 ingredientis 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.
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