Evidence for two exponent scaling in the random field Ising model

Novel methods were used to generate and analyze new 15 term high temperature series for both the (connected) susceptibility χ and the structure factor (disconnected susceptibility) χd for the random field Ising model with dimensionless coupling K=J/kT, in general dimension d. For both the bimodal and the Gaussian field distributions, with mean square field J2g, we find that (χd-χ)/K2gχ2=1 as T→Tc(g), for a range of [h2]=J2g and d=3,4,5. This confirms the exponent relation γ̄=2γ (where χd∼t-γ̄, χ∼t-γ, t=T-Tc) providing that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for γ.