Zeitschrift für Physik B Condensed Matter

, Volume 51, Issue 3, pp 237–249 | Cite as

One-dimensional spin glass with oscillating long-range interaction

  • M. V. Feigel'man
  • L. B. Ioffe


In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κVO cosQ x exp (−κ|x|), where κ≪cQ (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT c =cV0, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofTc (|τ≲(κ/c)2/3) and at very low temperaturesT≲κV0 when a gap appears in the distribution of the molecular fielsh ath≈0.


Heat Capacity Magnetic Susceptibility Spin Glass Density Wave Field Approximation 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • M. V. Feigel'man
    • 1
  • L. B. Ioffe
    • 1
  1. 1.L.D. Laudau Institute of Theoretical PhysicsThe Academy of Sciences of the USSRMoscowUSSR

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