We have examined zero-temperature metastable states of random-bond Ising models (random ferromagnets and spin glasses, in one, two, and three dimensions) for criticality (power-law sensitivity to single-spin-flip perturbations) and for limit cycles, with the following results. We found no evidence of criticality in metastable states obtained by quenches from high temperature. Near the metastability limit in a magnetic field, random ferromagnets in two and three dimensions are critical; the metastable states were generated by starting from a ground state and ramping a contrary field. Under a cycled magnetic field, both spin glasses and random ferromagnets quickly enter simple limit cycles.

• Received 21 April 1989

DOI:https://doi.org/10.1103/PhysRevB.40.6992