Short-range Ising spin glasses: a critical exponent study

The critical properties of short-range Ising spin-glass models, defined on diamond hierarchical lattices of graph fractal dimensions , and , and scaling factor 2, are studied via a method based on the Migdal–Kadanoff renormalization-group scheme. The order-parameter critical exponent is directly estimated from the data of the local Edwards–Anderson (EA) order parameter, obtained through an exact recursion procedure. The scaling of the EA order parameter, leading to estimates of the exponent of the correlation length is also performed. Four distinct initial distributions of the quenched coupling constants (Gaussian, bimodal, uniform and exponential) are considered. Deviations from a universal behavior are observed and analysed in the framework of the renormalized flow in a two-dimensional appropriate parameter space.