Scaling and chaos in periodic approximations to the two-dimensional Ising spin glass

Abstract

We approximate a 2D Ising spin glass by tiling an infinite square lattice with large identical unit cells. The interactions within the unit cell are random. Each such sample shows one or more critical points. We examine the scaling of the critical temperatures with unit cell size. Due to chaos, the correlations between unit cells can change sign with changing temperature. We also examine the scaling of this chaos. This chaos causes many samples to have multiple phase transitions, because the interaction between adjacent unit cells changes sign within the ordered phases.