Phase diagrams of random spin systems. I. Mean-field theory
- 20 September 1980
- journal article
- Published by IOP Publishing in Journal of Physics C: Solid State Physics
- Vol. 13 (26) , 5033-5057
- https://doi.org/10.1088/0022-3719/13/26/021
Abstract
The replica method is applied to Ising spin systems with random interactions. An effective Hamiltonian is derived for an arbitrary distribution of random bonds and the thermodynamic variational principle is used to evaluate the mean-field free energy. In the general case, the free energy depends explicitly on an infinite set of momenta ((si)k). For specific types of bond randomness results obtained previously are recovered. The phase diagram of the dilute Ising model with competing nearest-neighbour and next-nearest-neighbour interactions is worked out in detail. A spin glass phase is predicted at large enough dilution.Keywords
This publication has 24 references indexed in Scilit:
- On the relationship between long-time correlations and replica correlations in disordered systemsJournal of Physics A: General Physics, 1979
- Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactionsZeitschrift für Physik B Condensed Matter, 1979
- High-temperature expansion methods for Ising systems with quenched impuritiesPhysical Review B, 1979
- Replica symmetry and massless modes in the Ising spin glassJournal of Physics C: Solid State Physics, 1979
- Tricritical points in systems with random fieldsPhysical Review B, 1978
- Stability of the Sherrington-Kirkpatrick solution of a spin glass modelJournal of Physics A: General Physics, 1978
- Dilute bond Ising model and percolationJournal of Physics A: General Physics, 1976
- Theory of spin glassesJournal of Physics F: Metal Physics, 1975
- Critical properties of many-component systemsPhysical Review B, 1975
- Statistical Mechanical Theory of a Random Ferromagnetic SystemPhysical Review B, 1959