Universality in short-range Ising spin glasses

Abstract

The role of the distribution of coupling constants in the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a fixed-point distribution is found in an appropriated parameter space. The critical exponents β and ν are directly estimated from the data of the local Edwards–Anderson order parameters for the model defined on a diamond hierarchical lattice of fractal dimension d f =3. Four distinct initial distributions of coupling constants (Gaussian, bimodal, uniform and exponential) are considered; the results clearly indicate a universal behaviour.