Replica-symmetry breaking in dynamical glasses
Centro de Astrobiología, Instituto Nacional de Técnica Aeroespacial. Ctra. de Ajalvir Km.4, 28850 Torrejón de
2 Fritz-Haber-Institut der Max Planck Gesellschaft, Faradayweg 4-6, 14129 Berlin, Germany
Corresponding author: a firstname.lastname@example.org
Published online: 15 October 2001
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 all attractors of the system become identical in the thermodynamical limit up to variations of order , and thus replica symmetry is recovered for . In contrast to this, when fluctuating-field ensembles of initial conditions are chosen, replica symmetry remains broken in the thermodynamical limit.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.45.Xt – Synchronization; coupled oscillators / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001