New critical-point exponent and new scaling laws for short-range Ising spin glasses.

Abstract

We investigate the chaotic temperature dependence of the renormalized couplings in a short-range Ising spin glass. Some of our analytic and numerical results, obtained by the Migdal-Kadanoff renormalization scheme but argued to have general validity, differ from those of the scaling and droplet theory. First, chaos is present also at and above the critical temperature. Second, between ${\mathit{d}}_{\mathit{l}}$=2.46 (the lower critical dimension) and ${\mathit{d}}_{+}$=3.4, the chaos in the critical region is characterized by a new critical exponent ${\mathrm{\ensuremath{\zeta}}}_{\mathit{c}}$ that has hitherto escaped attention.