Ground States of Two-Dimensional Ising Spin Glasses: Fast Algorithms, Recent Developments and a Ferromagnet-Spin Glass Mixture

Using advanced numerical approaches based on optimization algorithms, much progress has been achieved for the study of the ground-state and low-temperature behavior of two-dimensional Ising spin glasses. Recent results led to a rather good understanding of these systems in the framework of the droplet-scaling theory. In this work, a pedagogical description of such an optimization-based approach is given and a short review of corresponding recent results is presented.