A solvable model of noisy coupled oscillators with fully random interactions

TL;DR

This paper presents a solvable spherical model of noisy coupled oscillators with random interactions, revealing how frequency distribution affects spin-glass transitions and providing insights into nonequilibrium glassy behavior.

Contribution

The authors develop a new solvable oscillator model using dynamical mean-field theory, analyzing the impact of frequency dispersion on glass transitions.

Findings

Finite frequency width suppresses finite-temperature spin-glass transition.

Zero-temperature spin-glass phase persists regardless of frequency dispersion.

Low-frequency singularity of correlation function conflicts with spherical constraint.

Abstract

We introduce a solvable spherical model of coupled oscillators with fully random interactions and distributed natural frequencies. Using the dynamical mean-field theory, we derive self-consistent equations for the steady-state response and correlation functions. We show that any finite width of the natural-frequency distribution suppresses the finite-temperature spin-glass transition, because the resulting low-frequency singularity of the correlation function is incompatible with the spherical constraint. At zero temperature, however, a spin-glass phase persists for arbitrary frequency dispersion. This residual zero-temperature glassiness is likely a special feature of the spherical dynamics and would be destroyed by local nonlinearities. The model thus provides a solvable oscillator framework for studying how nonequilibrium perturbations suppress finite-temperature glassy freezing.