Critical Properties of the Fuzzy Model

  • T. Kawasaki
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 43)


When the random spin system is quenched in the computer simulation experiment from the infinite to a temperature below the critical temperature T C , it should be inevitably trapped at one of the metastable states, depending on the random sequence in the Monte Carlo simulation. Then the random spin system shows similar behavior in some respects as the spin glass due to the fact that both have highly degenerate metastable states in the energy./l/,/2/ The randomness in the random spin system is usually introduced either in the coupling strength or in the site occupation. As far as we are concerned with the quadratic spin Hamiltonian, the more general introduction of the randomness may be achieved by the Fuzzy Spin Model(FSM)/3/, defined by
$$H = - \sum\limits_{ij} {{J_{ij}}{S_i}{S_j}} $$
where spins S j are Ising ones and uniformly random between 0 and 1 in their magnitudes site by site. The coupling J ij is set ferromagnetic (J ij = J) for nearest neighbor pairs only. The model is different from the Mattis model in that spin magnitude varies continuously between 0 and 1. We call static when spin magnitude once chosen is fixed forever, and time-dependent when spins fluctuate themselves in their magnitudes independently of the Hamiltonian.


Critical Temperature Metastable State Fuzzy Model Spin Glass Monte Carlo Step 
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  1. 1.
    A. E. Jacobs and C. M. Coram, Phys. Rev. B36 (1987),3844. M.Cieplak and T.R.Gawron, J. Phys. A20 (1987), 5657.ADSCrossRefGoogle Scholar
  2. 2.
    T. Kawasaki, Prog. Theor. Phys. 80 (1988) in press.Google Scholar
  3. 3.
    The model DTRM named in ref.2 is renamed as the Fuzzy Spin Model.Google Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • T. Kawasaki
    • 1
  1. 1.Department of Physics, College of Liberal ArtsKyoto UniversityKyotoJapan

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