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Journal of Mathematical Physics / Volume 29 / Issue 1

J. Math. Phys. 29, 21 (1988); http://dx.doi.org/10.1063/1.528176 (10 pages)

The analogy between spin glasses and Yang–Mills fluids

Darryl D. Holm1 and Boris A. Kupershmidt2

1Center for Nonlinear Studies and Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
2University of Tennessee Space Institute, Tullahoma, Tennessee 87388

(Received 21 July 1987; accepted 19 August 1987)

A dictionary of correspondence is established between the dynamical variables for spin‐glass fluid and Yang‐Mills plasma. The Lie‐algebraic interpretation of these variables is presented for the two theories. The noncanonical Poisson bracket for the Hamiltonian dynamics of an ideal spin glass is shown to be identical to that for the dynamics of a Yang–Mills fluid plasma, although the Hamiltonians differ for the two theories. This Poisson bracket is associated to the dual space of an infinite‐dimensional Lie algebra of semidirect‐product type.

KEYWORDS and PACS

Keywords

LASL, YANG−MILLS THEORY, CRYSTAL MODELS, SPIN GLASS STATE, MAGNETOHYDRODYNAMICS, HAMILTONIANS, LIE GROUPS, ORDER PARAMETERS, SINGULARITY, SOLID STATE PHYSICS, GAUGE INVARIANCE, INVARIANCE PRINCIPLES, EQUATIONS OF MOTION, GROUP THEORY

PACS

  • 02.20.Qs

    General properties, structure, and representation of Lie groups

  • 02.20.Sv

    Lie algebras of Lie groups

  • 52.30.-q

    Plasma dynamics and flow

  • 05.50.+q

    Lattice theory and statistics (Ising, Potts, etc.)

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.528176

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

For access to fully linked references, you need to log in.
    B. I. Halperin and W. M. Saslow, Phys. Rev. B 16, 2154 (1977).

    C. L. Henley, H. Sompolinsky, and B. I. Halperin, Phys. Rev. B 25, 5849 (1982).

    W. M. Saslow, Phys. Rev. B 27, 6873 (1983).

    N. D. Mermin, Rev. Mod. Phys. 51, 591 (1979).

    L. Michel, Rev. Mod. Phys. 52, 617 (1980).

    W. M. Saslow, Phys. Rev. B 22, 1174 (1980).

    J. P. Friedberg, Rev. Mod. Phys. 54, 801 (1982).



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