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

Abstract

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. Furthermore, original results are presented for a special type of system which combines a ferromagnetic sub lattice with a spin-glass sub lattice. Results for exact ground-state calculations up to system size N=1448×1448 are given. Past results of similar systems gave evidence that such a system might exhibit a spin-glass phase at finite temperatures. Nevertheless, the present results do not support this notion. But, for a suitable balance between ferromagnetic and ±J spin-glass couplings, extremely large finite-size effects occur. Thus, when considering intermediate system sizes, the system looks as if it orders. Furthermore, although the system exhibits only a discrete set of interactions, a power-law behavior for the stiffness energy can be observed clearly for a large range of system sizes. This is in contrast to past studies of systems with discrete sets of bond values.