One-dimensional spin glass with oscillating long-range interaction

M. V. Feigel'man, L. B. Ioffe

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15 Citations (Scopus)


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 cos Q x exp (-κ|x|), where κ≪c≪Q (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 point Tc=cV0, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional to T, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity of Tc (|τ≲(κ/c)2/3) and at very low temperatures T≲κV0 when a gap appears in the distribution of the molecular fiels h at h≈0.

Original languageEnglish
Pages (from-to)237-249
Number of pages13
JournalZeitschrift für Physik B Condensed Matter
Issue number3
Publication statusPublished - Sep 1983
Externally publishedYes


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