Existence of an oscillator glass in randomly coupled phase oscillators
In plain words
If oscillators are coupled with random signs, like spins in a spin glass, they may freeze into a disordered locked pattern, an oscillator glass. A peculiar transition seen in simulations in 1992 suggested this, but whether a true glass phase exists is unknown.
Precise statement
For dtheta_i/dt = $\omega_i$ + sum_j $J_{ij}$ sin(theta_j - theta_i) with Gaussian omega_i of unit variance and symmetric Gaussian couplings J_ij of variance $J^2/N$ (the Daido model), determine whether for $J$ above some $J_g$ the $N \to \infty$ dynamics has a frozen component, for example a nonzero limit of $C(\tau) = (1/2N) \operatorname{sum}_i \langle \cos(\theta_i(t+\tau) - \theta_i(t))\rangle$ as $\tau \to \infty$. The volcano transition near $J = 1.3$ (a change in shape of the local-field distribution) is established; its relation to a glass phase is the question. Answer: yes or no, with $J_g$.
What would settle it
A dynamical mean-field (cavity) solution at large J showing presence or absence of a persistent correlation plateau, confirmed by large-N simulations.
Status in the literature
Unverified note
A 2024 dynamical-cavity analysis explained the volcano transition and found no persistent correlation in the accessible range, arguing it does not imply a glass (arXiv:2310.09079).