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 {γ}{}=2{γ} (where χd{~}t^-γ, {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}.