Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions

Abstract

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 νincreases 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 νare affected by corrections to scaling.

arXiv comment4 pages, 3 figures

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• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
• Universality of the glassy transitions in the two-dimensional +- J Ising model
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