Distribution of barriers in spin glasses

We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain a large but finite number $N$ of spins. We apply this formalism to the Sherrington-Kirkpatrick model with finite $N$ and derive equations for the dynamical order parameters which allow “instanton” solutions describing transitions over the barriers separating metastable states. Specifically, we study these equations for a glass state that was obtained in a slow cooling process ending a little below $T_c$ and show that these equations allow “instanton” solutions which erase the response of the glass to the perturbations applied during the slow cooling process. The corresponding action of these solutions gives the energy of the barriers, we find that it scales as ${\tau }^6$ where $\tau$ is the reduced temperature.