The nature of attractors in an asymmetric spin glass with deterministic dynamics

H. Gutfreund*, J. D. Reger, A. P. Young

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

61 Scopus citations

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.

Original languageEnglish
Article number020
Pages (from-to)2775-2797
Number of pages23
JournalJournal of Physics A: Mathematical and General
Volume21
Issue number12
DOIs
StatePublished - 1988

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