The nature of attractors in an asymmetric spin glass with deterministic dynamics
- 21 June 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (12), 2775-2797
- https://doi.org/10.1088/0305-4470/21/12/020
Abstract
The authors study the attractors in an infinite-range Ising spin-glass model with deterministic dynamics where the interactions have asymmetry, specified by a parameter k. They find a duality relation between the attractors for models with asymmetry parameters k and 1/k. The attractors are fixed points or limit cycles of short length, except for k=1, at which the average cycle length diverges, reminiscent of a phase transition, and the model has many similarities to the random map model as well as to the infinite-range symmetric spin glass in thermal equilibrium, including the fact that a few attractors dominate the weight. The extent of this dominance varies from sample to sample and so is given by a non-trivial probability distribution, Pi (Y), which they compute numerically.Keywords
This publication has 15 references indexed in Scilit:
- Statistical properties of randomly broken objects and of multivalley structures in disordered systemsJournal of Physics A: General Physics, 1987
- Statistical mechanics of neural networks near saturationAnnals of Physics, 1987
- The random map model: a disordered model with deterministic dynamicsJournal de Physique, 1987
- Multivalley structure in Kauffman's model: analogy with spin glassesJournal of Physics A: General Physics, 1986
- Decreasing energy functions as a tool for studying threshold networksDiscrete Applied Mathematics, 1985
- Sample to sample fluctuations in the random energy modelJournal de Physique Lettres, 1985
- Emergent properties in random complex automataPhysica D: Nonlinear Phenomena, 1984
- Neural networks and physical systems with emergent collective computational abilities.Proceedings of the National Academy of Sciences, 1982
- Infinite-ranged models of spin-glassesPhysical Review B, 1978
- Metabolic stability and epigenesis in randomly constructed genetic netsJournal of Theoretical Biology, 1969