Critical Properties of a Simple Spin Glass Model

  • A. Aharony
  • Y. Imry


The spin glass state and the phase transitions into it have recently drawn much theoretical attention (1–9). In this phase the magnetic moments are supposed to be frozen but pointing in random directions, due to a competition between e.g. quenched ferromagnetic and antiferromagnetic interactions. In many systems of experimental interest (10–13) the magnetic ions are embedded in a metallic matrix and interacting with a RKKY coupling which becomes random in magnitude and sign due to the distribution of the interion spacing. However, in many theoretical models simpler short range random exchange interactions are assumed (2–9). At the present stage the theories appear not to be conclusive due to the use of mean field theory which neglects critical fluctuations and difficulties with the n = 0 (2,14) trick at low temperatures (7,8). The more recent renormalization group calculations (6) have used an expansion around d = 6 (d is the number of space dimensions) which would not lead to accurate results at d = 3. In view of those difficulties it seems worthwhile to have an exactly soluble model for the spin glass transition which although not realistic enough to correctly represent the systems under consideration may nevertheless give one some new insights on the problem.


Random Field Mattis Model Critical Property Spin Glass Random Field Model 
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Copyright information

© Plenum Press, New York 1977

Authors and Affiliations

  • A. Aharony
    • 1
  • Y. Imry
    • 2
    • 3
  1. 1.Tel Aviv UniversityRamat AvivIsrael
  2. 2.Tel Aviv UniversityRamat AvivIsrael
  3. 3.Brookhaven National LaboratoryUptonUSA

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