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Multiple Minimas In Glassy Random Matrix Models


  • Nivedita Deo


Certain models of structural glasses ref. [1, 2] map onto random matrix models. These random matrix models have gaps in their eigenvalue distribution. It turns out that matrix models with gaps in their eigenvalue distributions have the unusual property of multiple solutions or minimas of the free energy at the same point in phase space. I present evidence for the presence of multiple solutions in these models both analytically and numerically. The multiple solutions have different free energies and observable correlation functions, the differences arising at higher order in 1/N. The system can get trapped into different minimas depending upon the path traversed in phase space to reach a particular point. The thermodynamic limit also depends upon the sequence by which N is taken to infinity (e.g. odd or even N), reminicent of structure discussed in another model for glasses ref. [3]. Hence it would be of interest to study the landscape of these multiple solutions and determine whether it corresponds to a supercooled liquid or glass.

Suggested Citation

  • Nivedita Deo, 2000. "Multiple Minimas In Glassy Random Matrix Models," Working Papers 00-01-004, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:00-01-004

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    References listed on IDEAS

    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. Cristopher Moore & M. E. J. Newman, 2000. "Epidemics and Percolation in Small-World Networks," Working Papers 00-01-002, Santa Fe Institute.
    3. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    4. E. Roy Weintraub, 1992. "Introduction," History of Political Economy, Duke University Press, vol. 24(5), pages 3-12, Supplemen.
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    Structural glasses; random matrix models; multiple solutions.;

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