Steady state behavior of mechanically perturbed spin glasses and ferromagnets

A zero temperature dynamics of Ising spin glasses and ferromagnets on random graphs of finite connectivity is considered. Like granular media, these systems have an extensive entropy of metastable states. We consider the problem of what energy a randomly prepared spin system falls to before becoming stuck in a metastable state. We then introduce a tapping mechanism, analogous to that found in real experiments on granular media. This tapping, corresponding to flipping each spin with probability p simultaneously, leads to a stationary regime with a steady state energy E(p). We explicitly solve this problem for the one-dimensional ferromagnet and the +/-J spin glass, and carry out extensive numerical simulations for spin systems of higher connectivity. In addition our simulations on the ferromagnetic systems reveal a first order transition, whereas the usual thermodynamic transition on these graphs is second order.