Finite-size scaling in two-dimensional Ising spin glass models

Abstract

We study the finite-size behavior of two-dimensional spin-glass models. We consider the +-J model for two different values of the probability of the antiferromagnetic bonds and the model with Gaussian distributed couplings. The analysis of renormalization-group invariant quantities, the overlap susceptibility, and the two-point correlation function confirms that they belong to the same universality class. We analyze in detail the standard finite-size scaling limit in terms of TL^(1/nu) in the +-J model. We find that it holds asymptotically. This result is consistent with the low-temperature crossover scenario in which the crossover temperature, which separates the universal high-temperature region from the discrete low-temperature regime, scales as T_c(L) ~ L^(-theta_S) with theta_S \approx 0.5.

v2: added fig. 9b; 16 pages, 20 figs

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• Chaos and universality in two-dimensional Ising spin glasses
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• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Effective critical behavior of the two-dimensional Ising spin glass with bimodal interactions
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• Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

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