Metastate analysis of the ground states of two-dimensional Ising spin glasses

Abstract

Using an efficient polynomial-time ground state algorithm we investigate the Ising spin glass state at zero temperature in two dimensions. For large sizes, we show that the spin state in a central region is independent of the interactions far away, indicating a ``single-state" picture, presumably the droplet model. Surprisingly, a single power law describes corrections to this result down to the smallest sizes studied.

5 + epsilon pages, 4 figures. An extra figure has been added, and also a discussion on the possible connection between exponent we find, which controls the approach to the thermodynamic limit, and other exponents