# Correspondence between Phase Oscillator Network and Classical XY Model with the same random and frustrated interactions

## TL;DR

This paper explores the relationship between a phase oscillator network and the classical XY model with frustrated interactions, demonstrating their quantitative correspondence through numerical analysis of spin glass order parameters and local field distributions.

## Contribution

It establishes a quantitative correspondence between phase oscillator networks and XY models with frustrated interactions, supported by numerical simulations and mean field analysis.

## Key findings

- Parameter dependences of $q$ and local field distributions agree in both models.
- The correspondence relation effectively normalizes parameters across models.
- Time evolution of local fields reveals roles of synchronous and asynchronous oscillators.

## 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. As a result, we find that the parameter dependences of these quantities in both models agree fairly well 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 several quantities such as the time evolution of 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.