Bimodal Ising spin glass in two dimensions: The anomalous dimension η

摘要

Direct measurements of the spin glass correlation function G(R) for Gaussian and bimodal Ising spin glasses in dimension two have been carried out in the temperature region T ~ 1. In the Gaussian case the data are consistent with the known anomalous dimension value η = 0. For the bimodal spin glass in this temperature region T > T*(L), well above the crossover T*(L) to the ground-state-dominated regime, the effective exponent η is clearly nonzero and the data are consistent with the estimate η ~ 0.28(4) given by McMillan in 1983 from similar measurements. Measurements of the temperature dependence of the Binder cumulant U_4(T,L) and the normalized correlation length ξ(T,L)/L for the two models confirms the conclusion that the two-dimensional (2D) bimodal model has a nonzero effective η both below and above T*(L). The 2D bimodal and Gaussian interaction distribution Ising spin glasses are not in the same universality class.