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Monte Carlo Methods For First Order Phase Transitions: Some Recent Progress

Author

Listed:
  • KURT BINDER

    (Institut für Physik, Johannes-Gutenberg Universität, Staudingerweg 7, D-6500 Mainz, Germany)

  • KATHARINA VOLLMAYR

    (Institut für Physik, Johannes-Gutenberg Universität, Staudingerweg 7, D-6500 Mainz, Germany)

  • HANS-PETER DEUTSCH

    (Institut für Physik, Johannes-Gutenberg Universität, Staudingerweg 7, D-6500 Mainz, Germany)

  • JOSEPH D. REGER

    (Institut für Physik, Johannes-Gutenberg Universität, Staudingerweg 7, D-6500 Mainz, Germany)

  • MANFRED SCHEUCHER

    (Institut für Physik, Johannes-Gutenberg Universität, Staudingerweg 7, D-6500 Mainz, Germany)

  • DAVID P. LANDAU

    (Center for Simulational Physics, The University of Georgia, Athens, Georgia 30602, USA)

Abstract

This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model ind=3dimensions is treated as an example). First-order transitions are characterized by aminimumof the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures by a combination of histogram techniques and finite size scaling is described.As a final problem, we discuss the shift of the gas-liquid condensation in thin-film geometry confined between two parallel plates due to boundary fields (“capillary condensation”). Being interested in temperatures far below bulk criticality (e. g. near the wetting transition), special thermodynamic integration techniques are the method of choice, rather than the use of finite sizes scaling to map out the (asymmetric) phase diagram.

Suggested Citation

  • Kurt Binder & Katharina Vollmayr & Hans-Peter Deutsch & Joseph D. Reger & Manfred Scheucher & David P. Landau, 1992. "Monte Carlo Methods For First Order Phase Transitions: Some Recent Progress," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 3(05), pages 1025-1058.
    • Handle: RePEc:wsi:ijmpcx:v:03:y:1992:i:05:n:s0129183192000683
    DOI: 10.1142/S0129183192000683
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