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Gauge-invariant lattice gas for the microcanonical Ising model

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Abstract

We introduce a lattice gas for particles with discrete momenta (1, 0, −1) and local deterministic microdynamics, which exactly reproduces Creutz's microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.

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Authors and Affiliations

  1. Electrical, Computer and Systems Department, and Department of Physics, Boston University, Boston, Massachusetts

    Richard C. Brower

  2. Institute for Computational Studies, Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada

    K. J. M. Moriarty

  3. Institute for Advanced Study and John von Neumann National Supercomputer Center, Princeton, New Jersey

    K. J. M. Moriarty

  4. Physics Department, Virginia Polytechnic Institute and State University, Blacksburg, Virginia

    Peter Orland

  5. Physics Department and Center for Polymer Studies, Boston University, Boston, Massachusetts

    Pablo Tamayo

Authors
  1. Richard C. Brower
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  2. K. J. M. Moriarty
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  3. Peter Orland
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  4. Pablo Tamayo
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Brower, R.C., Moriarty, K.J.M., Orland, P. et al. Gauge-invariant lattice gas for the microcanonical Ising model. J Stat Phys 58, 141–157 (1990). https://doi.org/10.1007/BF01020289

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  • DOI: https://doi.org/10.1007/BF01020289

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