The Heat Bath Monte Carlo Algorithm for the Ising Model of Ferromagnetism

POSTER

Abstract

The mathematical theory of Markov chains is placed in the context of the Ising model of ferromagnetism, an important problem in statistical physics. Although not a Markov chain itself, the two-dimensional Ising model can be simulated with the heat bath algorithm, which treats the Ising model as a Markov Chain. A Matlab program and variations were written that use Monte Carlo simulation and the heat bath algorithm to compute quantities arising in the Ising model. Results from this method were then compared to those derived from the mathematical definition of the Ising Model. Based on the agreement of results, it can be concluded that the heat bath Markov Chain method is a convenient and valid method to simulate the two-dimensional Ising model.

Authors

  • Christopher Lemon

    Ohio Northern University

  • Doug Petkie

    AFRL/RX, AFRL/RX, Systran Systems Inc, UCSD, Los Alamos National Laboratory, Ohio Northern University, BFS, Germany, Florida State University, Monmouth College, Ohio Wesleyan University, Department of Chemical and Biomolecular Engineering, The University of Akron, Physics Department, John Carroll University, Department of Chemistry, Knight Chemical Laboratories, The University of Akron, Australian National University, Miami University, Oxford, OH, University of Cincinnati, University of Findlay, Naval Research Laboratory, Washington, DC 20375, Cleveland State University, Health Sciences Dept, Cleveland State University, Physics Dept, Cleveland State University, Bucknell University, Wright State University, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, Wright State University, Department of Physics, University of Puerto Rico, Department of Mechanical Engineer, Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB and UES, Inc., Department of Environmental Science and Policy, School of Science, Marist College, Poughkeepsie, NY 12601, USA, AFRL/711 HPW, EPA Sustainable Technology Division, University of Akron, Rose-Hulman Institute of Technology, Harvard University, LSU, Ohio University, Wittenberg University, Student