Scaling in Spin-Glasses

Abstract

Many results of the mean-field theory of spin-glasses violate simple scaling laws, including the magnetic field dependence of the transition lines, crossover effects of random anisotropy, and critical behavior in the ordered phase. These violations arise from two dangerously irrelevant variables. Below eight dimensions some mean-field exponents change and at $d=6$ scaling is restored. Below $d=6$ all scaling laws should be valid implying that the critical properties of real spin-glasses should be simpler than in mean-field theory. Experimental consequences are discussed.