Finite-Time-Finite-Size Scaling of the Kuramoto Oscillators

Abstract

Phase transition in its strict sense can only be observed in an infinite system, for which equilibration takes an infinitely long time at criticality. In numerical simulations, we are often limited both by the finiteness of the system size and by the finiteness of the observation time scale. We propose that one can overcome this barrier by measuring the nonequilibrium temporal relaxation for finite systems and by applying the finite-time-finite-size scaling (FTFSS) which systematically uses two scaling variables, one temporal and the other spatial. The FTFSS method yields a smooth scaling surface, and the conventional finite-size scaling curves can be viewed as proper cross sections of the surface. The validity of our FTFSS method is tested for the synchronization transition of Kuramoto models in the globally-coupled structure and in the small-world network structure. Our FTFSS method is also applied to the Monte-Carlo dynamics of the globally-coupled q-state clock model.

12 pages(main text: 5 pages, supplemental material: 7 pages), 9 figures(main text: 4 figures, supplemental material: 5 figures), one table in supplemental material

References in corpus (4)

• Analysis of a power grid using the Kuramoto-like model
• Entrainment transition in populations of random frequency oscillators
• How to suppress undesired synchronization
• Double stochastic resonance in the mean-field $q$-state clock models

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• The Kuramoto model in complex networks
• Critical dynamics of the Kuramoto model on sparse random networks
• Universality classes of generalized epidemic process on random networks
• Shadows of the SIS immortality transition in small networks
• One node driving synchronisation
• Predicting the Oscillatory Regimes of Global Synchrony Induced by Secondary Clusters
• Anomalous Dynamical Scaling at Topological Quantum Criticality