Two-scale-factor universality and the renormalization group

P. C. Hohenberg*, A. Aharony, B. I. Halperin, E. D. Siggia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 He4, 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.

Original languageEnglish
Pages (from-to)2986-2996
Number of pages11
JournalPhysical Review B-Condensed Matter
Issue number7
StatePublished - 1976


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