Abstract
Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions d using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents (ζ,γ,δ,μ) are obtained by free-energy minimization. Scaling between different bar widths provides the renormalization group (RG) transformation. Its consequences are i) criticality at h = T = 0 in d ⩽ 2 with correlation length ξ(h,T) diverging like ξ(h,0) ∝ h−2/(2 − d) for d < 2 and ξ(h,0) ∝ exp [1/(c1γhγ)] for d = 2, where c1 is a decoration constant; ii) criticality in d = 2 + ε dimensions at T = 0, h* = (ε/2c1)1/γ, where ξ ∝ [(s − s*)/s]−2ε/γ, s ≡ hγ. Finite-temperature generalizations are outlined. Numerical transfer matrix calculations and results from a ground-state algorithm adapted for strips in d = 2 confirm the ingredients which provide the RG description.