Replica-symmetry breaking in dynamical glasses

Details Replica-symmetry breaking in dynamical glasses Replica-symmetry breaking in dynamical glasses

2001-07-12

arxiv.org/abs/cond-mat/0107249v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 18 figures

Scientific paper

10.1007/s100510170041

Systems of globally coupled logistic maps (GCLM) can display complex collective behaviour characterized by the formation of synchronous clusters. In the dynamical clustering regime, such systems possess a large number of coexisting attractors and might be viewed as dynamical glasses. Glass properties of GCLM in the thermodynamical limit of large system sizes $N$ are investigated. Replicas, representing orbits that start from various initial conditions, are introduced and distributions of their overlaps are numerically determined. We show that for fixed-field ensembles of initial conditions, as used in previous numerical studies, all attractors of the system become identical in the thermodynamical limit up to variations of order $1/\sqrt{N}$ because the initial value of the coupling field is characterized by vanishing fluctuations, and thus replica symmetry is recovered for $N\to \infty $. In contrast to this, when random-field ensembles of initial conditions are chosen, replica symmetry remains broken in the thermodynamical limit.

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