TY - JOUR

T1 - Two-scale-factor universality and the renormalization group

AU - Hohenberg, P. C.

AU - Aharony, A.

AU - Halperin, B. I.

AU - Siggia, E. D.

N1 - Funding Information:
Work at the University of Pennsylvania supported in part by the National Science Foundation under Grant No. GH34556.

PY - 1976/1/1

Y1 - 1976/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=24044502681&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.13.2986

DO - 10.1103/PhysRevB.13.2986

M3 - Article

AN - SCOPUS:24044502681

VL - 13

SP - 2986

EP - 2996

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 7

ER -