Correlation length of the two-dimensional Ising spin glass with Gaussian interactions

We study the correlation length of the two-dimensional Ising spin glass with a Gaussian distribution of interactions, using an efficient Monte Carlo algorithm, proposed by Houdayer, that allows larger sizes and lower temperatures to be studied than was possible before. We find that the “effective” value of the bulk correlation length exponent ν increases as the temperature is lowered, and, at low temperatures, apparently approaches −1∕θ, where θ≃−0.29 is the stiffness exponent obtained at zero temperature. This means scaling is satisfied and earlier results at higher temperatures that find a smaller value for ν are affected by corrections to scaling.