Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass

  • M. Scheucher
  • J. D. Reger
  • K. Binder
  • A. P. Young
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 53)

Abstract

During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. The model is defined by the following Hamiltonian
$$H = - \sum\limits_{ < i,j > } {{J_{ij}}} {\delta _{ni,nj}}\,;\,{n_i}\, \in \{ 1,2, \cdots ,p\} $$
where the sum is over all nearest neighbor pairs of the simple cubic lattice. The couplings are Gaussian with zero mean and variance one, which merely sets the temperature scale. We further restrict to p = 3.

Keywords

Entropy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D.J. Gross, I. Kanter and H. Sompolinsky, Phys. Rev. Lett. 55, 304 (1985)ADSCrossRefGoogle Scholar
  2. [2]
    K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986)ADSCrossRefGoogle Scholar
  3. [3]
    R.N. Bhatt and A.P. Young, Phys. Rev. Lett. 54, 924 (1985); Phys. Rev. B37, 5606 (1988) and in Proc. Heidelberg Colloquium on Glassy Dynamics (L. van Hemmen and I. Morgenstern, eds.), p.215, (Springer, Berlin 1987)Google Scholar
  4. [4]
    W.L. McMillan, J. Phys. C17, 3179 (1984)ADSGoogle Scholar
  5. [5]
    Further evidence for a highly degenerate ground state comes from a numerical transfer-matrix calculation on 2 dimensional strips where we obtained a finite zero temperature entropy for the Gaussian Potts glass (to be published).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • M. Scheucher
    • 1
  • J. D. Reger
    • 1
  • K. Binder
    • 1
  • A. P. Young
    • 2
  1. 1.Institut für PhysikUniversität MainzMainzFed. Rep. of Germany
  2. 2.Physics DepartmentUniversity of CaliforniaSanta CruzUSA

Personalised recommendations