Short-range Ising spin glasses: a critical exponent study

Abstract

The critical properties of short-range Ising spin-glass models, defined on diamond hierarchical lattices of graph fractal dimensions 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 behavior are observed and analysed in the framework of the renormalized flow in a two-dimensional appropriate parameter space.