Barriers in thep-Spin Interacting Spin-Glass Model: The Dynamical Approach

We investigate the barriers separating metastable states in the spherical $p-\mathrm{spin}$ glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.