2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155735As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and applied to two-dimensional Ising spin glasses. The algorithm combines the Pfaffian and matching approaches to directly strip droplet excitations from an excited state. Extended ground states in Ising spin glasses on a torus, which are optimized over all boundary conditions, are used to compute precise values for ground state energy densities.4 pages, 2 figures; minor clarificationsDisordered Systems and Neural NetworksStatistical Mechanicstext