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

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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 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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Authors and Affiliations

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

    K. Bindera

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  1. K. Bindera
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Bindera, K. Monte Carlo methods for the study of phase transitions and phase equilibria. Eur. Phys. J. B 64, 307–314 (2008). https://doi.org/10.1140/epjb/e2008-00109-x

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  • DOI: https://doi.org/10.1140/epjb/e2008-00109-x

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