Two-scale-factor universality and the renormalization group

The hypothesis of two-scale-factor universality, originally proposed by Stauffer, Ferer, and Wortis, is shown to follow from the renormalization-group approach, for systems close to their critical point. Values of the universal ratios involving correlation length and specific-heat amplitudes are obtained from the ε expansion, for Ising, X-Y, and Heisenberg models. In the latter two cases the correlation function has a power-law behavior at large distances below Tc, and the (transverse) correlation length is defined in terms of the stiffness constant ρₛ. Experimental values of the correlation lengths and amplitude ratios are determined for superfluid ⁴He, which is X-Y-like, and for the Heisenberg antiferromagnet RbMnF₃. Comparisons are made between the values of the amplitude ratios coming from ε expansions, series, and experiments.