Short Range Ising Spin Glasses: a critical exponent study

The critical properties of short-range Ising spin-glass models, defined on a diamond hierarchical lattice of graph fractal dimension df = 2.58, 3, and 4, and scaling factor 2 are studied via a method based on the Migdal-Kadanoff renormalization-group scheme. The order parameter critical exponent β 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 ν 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 behaviour are observed and analysed in the framework of the renormalized flow in a two dimensional appropriate parameter space. 05.50.+q, 75.10.Nr and 64.60.Fr Typeset using REVTEX