Parallel multicanonical study of the three-dimensional Blume-Capel model

Johannes Zierenberg, Nikolaos G. Fytas, Wolfhard Janke

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    Abstract

    We study the thermodynamic properties of the three-dimensional Blume-Capel model on the simple cubic lattice by means of computer simulations. In particular, we implement a parallelized variant of the multicanonical approach and perform simulations by keeping a constant temperature and crossing the phase boundary along the crystal-field axis. We obtain numerical data for several temperatures in both the first- and second-order regime of the model. Finite-size scaling analyses provide us with transition points and the dimensional scaling behavior in the numerically demanding first-order regime, as well as a clear verification of the expected Ising universality in the respective second-order regime. Finally, we discuss the scaling behavior in the vicinity of the tricritical point. Publisher statement: Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society Article available from: http://link.aps.org/abstract/PRE/v91/i3/2015/e032126
    Original languageEnglish
    Article number032126
    JournalPhysical Review E
    Volume91
    Issue number3
    DOIs
    Publication statusPublished - 18 Mar 2015

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    Blume-Capel Model
    Scaling Behavior
    First-order
    scaling
    Three-dimensional
    Tricritical Point
    Thermodynamic Properties
    Finite-size Scaling
    Ising
    Universality
    Crystal
    Computer Simulation
    cubic lattices
    readers
    transition points
    crystal field theory
    thermodynamic properties
    computerized simulation
    Simulation
    temperature

    Bibliographical note

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    Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society

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    Parallel multicanonical study of the three-dimensional Blume-Capel model. / Zierenberg, Johannes; Fytas, Nikolaos G.; Janke, Wolfhard.

    In: Physical Review E, Vol. 91, No. 3, 032126, 18.03.2015.

    Research output: Contribution to journal › Article

    Zierenberg, J, Fytas, NG & Janke, W 2015, 'Parallel multicanonical study of the three-dimensional Blume-Capel model' Physical Review E, vol. 91, no. 3, 032126. https://doi.org/10.1103/PhysRevE.91.032126
    Zierenberg J, Fytas NG, Janke W. Parallel multicanonical study of the three-dimensional Blume-Capel model. Physical Review E. 2015 Mar 18;91(3). 032126. https://doi.org/10.1103/PhysRevE.91.032126
    Zierenberg, Johannes ; Fytas, Nikolaos G. ; Janke, Wolfhard. / Parallel multicanonical study of the three-dimensional Blume-Capel model. In: Physical Review E. 2015 ; Vol. 91, No. 3.
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    N2 - We study the thermodynamic properties of the three-dimensional Blume-Capel model on the simple cubic lattice by means of computer simulations. In particular, we implement a parallelized variant of the multicanonical approach and perform simulations by keeping a constant temperature and crossing the phase boundary along the crystal-field axis. We obtain numerical data for several temperatures in both the first- and second-order regime of the model. Finite-size scaling analyses provide us with transition points and the dimensional scaling behavior in the numerically demanding first-order regime, as well as a clear verification of the expected Ising universality in the respective second-order regime. Finally, we discuss the scaling behavior in the vicinity of the tricritical point. Publisher statement: Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society Article available from: http://link.aps.org/abstract/PRE/v91/i3/2015/e032126

    AB - We study the thermodynamic properties of the three-dimensional Blume-Capel model on the simple cubic lattice by means of computer simulations. In particular, we implement a parallelized variant of the multicanonical approach and perform simulations by keeping a constant temperature and crossing the phase boundary along the crystal-field axis. We obtain numerical data for several temperatures in both the first- and second-order regime of the model. Finite-size scaling analyses provide us with transition points and the dimensional scaling behavior in the numerically demanding first-order regime, as well as a clear verification of the expected Ising universality in the respective second-order regime. Finally, we discuss the scaling behavior in the vicinity of the tricritical point. Publisher statement: Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society Article available from: http://link.aps.org/abstract/PRE/v91/i3/2015/e032126

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