Critical behavior and universality in Levy spin glasses

Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster updates, we show that Ising spin glasses with Levy-distributed interactions share the same universality class as Ising spin glasses with Gaussian or bimodal-distributed interactions. Corrections to scaling are large for Levy spin glasses. In order to overcome these and show that the critical exponents agree with the Gaussian case, we perform an extended scaling of the two-point finite size correlation length and the spin glass susceptibility. Furthermore, we compute the critical temperature and compare its dependence on the disorder distribution width to recent analytical predictions [J. Stat. Mech. (2008) P04006].