Relaxation height in energy landscapes: an application to multiple metastable states
Lattice dynamics that is driven by the energy landscape, typically involves trajectories with a decreasing energy. The temperature parameter partially quantifies the reverse phenomenon of jumps against the energy drift. The smallness of the probability to execute such moves is controlled by the cost function. In the low temperature dynamics of the statistical mechanics lattice systems, in addition to the structure of the absolute minima of energy (ground states) one needs to estimate the maximal cost barrier, here called the relaxation height, to be overcome if the set of ground states is to be reached by starting from any possible state of the system. The paper addresses a fairly general optimization method aiming at an explicit computation of the relaxation height for models with multiple metastable states. Sufficient conditions to identify the metastable states are established. As a physical application, the Blume-Capel model for a particular magnetic system is considered. The transition time from the metastable states to the stable state is estimated in probability. The set of critical configurations is identified, that represent the minimal gate for the transition.
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