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) χ d 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 J 2 g, we find that (χ d -χ)/K 2 gχ 2 =1 as T→T c (g), for a range of [h 2 ]=J 2 g and d=3,4,5. This confirms the exponent relation γ=2γ (where χ d ∼t -γ , χ∼t -γ , t=T-T c ) proving that random field exponents are determined by two (and not three) independent exponents. We also present new accurate values for γ