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Phase diagram of Cu-Au-type alloys

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Abstract

We investigate the ordering phase diagram of an binary alloy on a face centered cubic lattice. In Ising spin language the nearest-neighbor interactions are antiferromagnetic with strengthJ, the next-nearest-neighbor interactions are ferromagnetic with strength αJ, and the external magnetic field ish. Forα > 0 and allh, the ground state is only finitely degenerate, so Pirogov-Sinai theory gives the exact form of the phase diagram in the limit of vanishing temperature. Forα=0 and vhv⩽ 12J the ground state is infinitely degenerate, and indeed the zero temperature entropy is nonvanishing at the four “super-degenerate” pointsh=± 47 or ±1Z7. We investigate the finite temperature behavior of the model using Monte Carlo simulations and (forα=0) low temperature expansions. The most interesting portions of the phase diagram are those near the superdegenerate points. We rigorously map these points onto certain “hard constraint” lattice gases, but can draw no firm conclusions concerning the phase diagram in their vicinity.

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Author notes

  1. Mohan K. Phani

    Present address: Department of Physics, Indian Institute of Science, 560012, Bengalore, India

Authors and Affiliations

  1. Departments of Mathematics and Physics, Rutgers University, 08903, New Brunswick, New Jersey

    Joel L. Lebowitz, Mohan K. Phani & Daniel F. Styer

Authors
  1. Joel L. Lebowitz
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  2. Mohan K. Phani
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  3. Daniel F. Styer
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Additional information

Supported in part by the National Science Foundation through Grant No. DMR81-14726. The simulations were carried out at the Center for Materials Science at Los Alamos National Laboratory.

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Lebowitz, J.L., Phani, M.K. & Styer, D.F. Phase diagram of Cu-Au-type alloys. J Stat Phys 38, 413–431 (1985). https://doi.org/10.1007/BF01017871

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  • DOI: https://doi.org/10.1007/BF01017871

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