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

Toldin, Francesco Parisen and Pelissetto, Andrea and Vicari, Ettore (2011) Finite-size scaling in two-dimensional Ising spin glass models. Physical review. E, Statistical, nonlinear, and soft matter physics, 84 . 051116. ISSN 1550-2376

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.

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