Glassy properties of frustrated arrays of nonlinear devices.

We study linear arrays of different number of quartic oscillators shaped in the form of a ring when Gaussian noise (temperature) is added. Frustration is introduced through periodic boundary conditions and repulsive, directional interactions between neighboring oscillators. We show that these systems have similar dynamic properties than the arrays of fluxgates magnetometers. We find that there is a critical number of oscillators separating the regimes arising for systems with few and many oscillators and show that they reach an optimum ordering for a nonvanishing temperature. We also find that they have a relaxation process with an infinite mean life that is typical of glassy systems.