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Microcanonical Determination Of The Order Parameter Critical Exponent

Author

Listed:
  • ALFRED HÜLLER

    (Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, D – 91058 Erlangen, Germany)

  • MICHEL PLEIMLING

    (Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, D – 91058 Erlangen, Germany)

Abstract

A highly efficient Monte Carlo method for the calculation of the density of states of classical spin systems is presented. As an application, we investigate the density of statesΩN(E, M)of two- and three-dimensional Ising models withNspins as a function of energyEand magnetizationM. For a fixed energy lower than a critical valueEc,Nthe density of states exhibits two sharp maxima atM = ± Msp(E)which define the microcanonical spontaneous magnetization. An analysis of the formMsp(E) ∝ (Ec, ∞- E)βεyields very good results for the critical exponent βε, thus demonstrating that critical exponents can be determined by analyzing directly the density of states of finite systems.

Suggested Citation

  • Alfred Hüller & Michel Pleimling, 2002. "Microcanonical Determination Of The Order Parameter Critical Exponent," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(07), pages 947-956.
    • Handle: RePEc:wsi:ijmpcx:v:13:y:2002:i:07:n:s0129183102003693
    DOI: 10.1142/S0129183102003693
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    Cited by:

    1. G. Palma & A. Riveros, 2021. "General method to sample systems in the microcanonical ensemble using Monte Carlo simulations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(1), pages 1-9, January.
    2. Sastre, Francisco, 2021. "Critical point determination from probability distribution functions in the three dimensional Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

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