Critical behavior and universality in Lévy spin glasses

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Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster updates, we show that Ising spin glasses with L\'evy-distributed interactions share the same universality class as Ising spin glasses with Gaussian or bimodal-distributed interactions. Corrections to scaling are large for L\'evy spin glasses. To overcome these and show that the critical exponents agree with the bimodal and 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 with recent analytical predictions [J. Stat. Mech. (2008) P04006].