Determining energy barriers by iterated optimization: The two-dimensional Ising spin glass

Energy barriers determine the dynamics in many physical systems like structural glasses, disordered spin systems, or proteins. Here we present an approach, based on subdividing the configuration space in a hierarchical manner, which leads to upper and lower bounds for the energy barrier separating two configurations. As an application, we consider Ising spin glasses, where the energy barriers which need to be surmounted in order to flip a compact region of spins of linear dimension L are expected to scale as L-psi. The fundamental operation needed is to perform a constrained energy optimization. For the the two-dimensional Ising spin glass we use an efficient combinatorial matching algorithm, resulting in the nontrivial numerical bounds 0.25 < 0.54.