Partially and Fully Frustrated Coupled Oscillators With Random Pinning Fields

TL;DR

This paper investigates two models of frustrated coupled oscillators with random pinning fields, analyzing their equilibrium properties and phase transitions using the replica method, supported by simulations.

Contribution

It introduces and compares two disordered oscillator models with different frustration types, providing explicit predictions for their phase behavior under random pinning fields.

Findings

Pinning fields break symmetry between models.

Models behave identically without pinning fields.

Simulation data support theoretical predictions.

Abstract

We have studied two specific models of frustrated and disordered coupled Kuramoto oscillators, all driven with the same natural frequency, in the presence of random external pinning fields. Our models are structurally similar, but differ in their degree of bond frustration and in their finite size ground state properties (one has random ferro- and anti-ferromagnetic interactions; the other has random chiral interactions). We have calculated the equilibrium properties of both models in the thermodynamic limit using the replica method, with emphasis on the role played by symmetries of the pinning field distribution, leading to explicit predictions for observables, transitions, and phase diagrams. For absent pinning fields our two models are found to behave identically, but pinning fields (provided with appropriate statistical properties) break this symmetry. Simulation data lend satisfactory support to our theoretical predictions.