Correspondence between phase oscillator network and classical XY model with the same random and frustrated interactions.

Abstract

We study correspondence between a phase oscillator network with distributed natural frequencies and a classical XY model at finite temperatures with the same random and frustrated interactions used in the Sherrington-Kirkpatrick model. We perform numerical calculations of the spin glass order parameter q and the distributions of the local fields P(R), where R is the amplitude of the local field. As a result, we find that the parameter dependences of P(R) in both models agree fairly well in all ranges of parameters in the spin glass phase and those of q agree at least for lower values of parameters in the spin glass phase, if parameters are normalized by using the previously obtained correspondence relation between two models with the same other types of interactions. Furthermore, we numerically calculate the time evolution of quantities such as the instantaneous local field in the phase oscillator network in order to study the roles of synchronous and asynchronous oscillators. We also study the self-consistent equation of the local fields in the oscillator network and XY model derived by the mean-field approximation.