On the 'naive' mean-field equations for spin glasses
- 20 November 1986
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 19 (32) , 6389-6406
- https://doi.org/10.1088/0022-3719/19/32/014
Abstract
A model is introduced for which the 'naive' mean-field equations (NMFE) for an Ising system, mi=tanh ( beta Sigma jJijmj+ beta hi), became exact in any dimension. The model is solved for the infinite-range Ising spin glass (i) starting from the Hamiltonian and using the replica method without replica symmetry breaking, and (ii) starting directly from the NMFE using the method of Sompolinsky (1983). The solution is qualitatively similar to that of the Sherrington-Kirkpatrick model (1975). The Glauber model (1963) for the dynamics of the system is also discussed; the spin autocorrelation function exhibits a t-1/2 decay everywhere in the ordered phase.Keywords
This publication has 23 references indexed in Scilit:
- TAP free energy structure of SK spin glassesJournal of Physics C: Solid State Physics, 1985
- Irreversibility of infinite range spin glassesJournal of Applied Physics, 1984
- Irreversibility and metastability in spin-glasses. II. Heisenberg modelPhysical Review B, 1983
- Irreversibility and metastability in spin-glasses. I. Ising modelPhysical Review B, 1983
- Free-energy surface of spin-glasses: Thouless-Anderson-Palmer and Bethe-Peierls-Weiss modelsPhysical Review B, 1983
- Two- and three-spin cluster theory of spin-glassesPhysical Review B, 1981
- Evidence for massless modes in the 'solvable model' of a spin glassJournal of Physics C: Solid State Physics, 1979
- Solution of the long-range gaussian-random Ising modelZeitschrift für Physik B Condensed Matter, 1978
- Solution of 'Solvable model of a spin glass'Philosophical Magazine, 1977
- Solvable Model of a Spin-GlassPhysical Review Letters, 1975