Properties of the two-dimensional random-bond [Formula Presented] Ising spin glass

Abstract

We develop an exact gauge-invariant method for studying the two-dimensional [Formula Presented] spin glass. It is applied to the case of an arbitrary concentration of [Formula Presented] positive and p negative bonds and is thus a generalization of the more commonly studied [Formula Presented] model. The ground-state properties are examined and in particular it is shown that the spin correlation exponent η remains constant over the range [Formula Presented] The value obtained is [Formula Presented] A wide range of values for η is quoted in the literature. We indicate possible reasons for the discrepancies and indicate that there are potential advantages in doing calculations at concentrations markedly lower than 50%. © 1998 The American Physical Society.