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

Area of Science:

• Statistical mechanics
• Complex systems
• Condensed matter physics

Background:

• The Sherrington-Kirkpatrick model is a standard for studying spin glasses.
• Phase oscillator networks exhibit complex dynamics relevant to various physical phenomena.

Purpose of the Study:

• To investigate the correspondence between phase oscillator networks and the XY model.
• To analyze spin glass properties using these interconnected models.
• To understand the roles of synchronous and asynchronous oscillators.

Main Methods:

• Numerical calculations of the spin glass order parameter (q).
• Analysis of local field distributions P(R).
• Numerical computation of time evolution for local fields.
• Mean-field approximation for self-consistent equations.

Main Results:

• Parameter dependencies of P(R) agree well in the spin glass phase.
• Parameter dependencies of q agree in the spin glass phase for lower parameter values.
• Insights into the roles of synchronous and asynchronous oscillators were gained.

Conclusions:

• A strong correspondence exists between phase oscillator networks and XY models with frustrated interactions.
• The findings validate normalized parameter relations for comparing these models.
• The study provides a framework for analyzing complex oscillatory systems through established statistical models.