Tuning the Metropolis algorithm

ORAL

Abstract

The Metropolis algorithm is a method for simulating equilibrium states of systems. Metropolis Monte Carlo simulations are commonly used to explore material properties, such as transition temperatures. For complex systems, statistical convergence can be hard to achieve, making the results ambiguous. Increasing your sample size will increase the likelihood of convergence, but if the simulation already takes 20 days, increasing the runtime by an order of magnitude is impractical. In an effort to find the best ways to improve simulation results without just increasing runtime, we explored the effects of various computational parameters on a test case, 2D binary alloy model. These parameters include the number of random samples (called Monte Carlo steps), lattice size, and temperature step-size. We hope to use these results to improve simulations of more complex systems in the future.

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Authors

  • Spencer Hart

    Brigham Young University

  • John Colton

    Brigham Young University Dept. of Physics and Astronomy, Brigham Young University, None, The College of William and Mary/Jefferson Lab, Brigham Young University-Idaho, Blue Ridge Research and Consulting LLC, Air Force Research Laboratory - Wright Patterson Air Force Base, Brigham Young Univ - Provo, Blue Ridge Research and Consulting, University of Utah, SRI International, Utah State University, Utah Valley University, Los Alamos National Laboratory, Professor, Graduate, United States Air Force Academy, Arizona State Univ, SiO2 NanoTech, Entrepix Inc, AFRL, Advisor, Brigham Young University- Provo, University of New Mexico, Univ of Utah, University of Wisconsin -- Madison, New Mexico Tech Physics Dept., Retired, Department of Physics and Astronomy, University of Utah, Department of Physics \& Astronomy, University of Hawai'i, JILA and University of Colorado, Boulder, National Institute of Standards and Technology, Boulder, University of Colorado, Boulder, Lawrence Berkeley National Laboratory, National Institute of Standards and Technology, Space Dynamics Lab, New Mexico Tech, BYU Professor, Brigham Young University -- Provo, Northern Arizona University, University of Colorado Boulder, Colorado State University, University of Utah, Department of Physics, New Mexico State University

  • John Colton

    Brigham Young University Dept. of Physics and Astronomy, Brigham Young University, None, The College of William and Mary/Jefferson Lab, Brigham Young University-Idaho, Blue Ridge Research and Consulting LLC, Air Force Research Laboratory - Wright Patterson Air Force Base, Brigham Young Univ - Provo, Blue Ridge Research and Consulting, University of Utah, SRI International, Utah State University, Utah Valley University, Los Alamos National Laboratory, Professor, Graduate, United States Air Force Academy, Arizona State Univ, SiO2 NanoTech, Entrepix Inc, AFRL, Advisor, Brigham Young University- Provo, University of New Mexico, Univ of Utah, University of Wisconsin -- Madison, New Mexico Tech Physics Dept., Retired, Department of Physics and Astronomy, University of Utah, Department of Physics \& Astronomy, University of Hawai'i, JILA and University of Colorado, Boulder, National Institute of Standards and Technology, Boulder, University of Colorado, Boulder, Lawrence Berkeley National Laboratory, National Institute of Standards and Technology, Space Dynamics Lab, New Mexico Tech, BYU Professor, Brigham Young University -- Provo, Northern Arizona University, University of Colorado Boulder, Colorado State University, University of Utah, Department of Physics, New Mexico State University