Scaling function for two-point correlations. II. Expansion to order 1n

Amnon Aharony*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The zero-field two-point correlation function of an n-vector system in d dimensions is calculated to order 1n for Tc and 2<d<4. The critical-point scaling function is obtained as a closed cutoff-independent integral. As t=(T-Tc)Tc→0 at fixed wave vector q, the variation of the Fourier transform of the correlation function is E^1(q)t1-α+E^2(q)t+E^3(q)t2+a, where α is the specific-heat exponent and E^2, E^3 are of order 1n. At d=3 the term t2 is modified by logarithmic corrections. As q→0 at fixed nonzero t, deviations of the scaling function from the Ornstein-Zernike form (1+ξ2q2)-1 are of order 10-3ξ4q4n. Results are compared with high-temperature series-expansion estimates and with the ε-expansion results of previous work.

Original languageEnglish
Pages (from-to)2834-2844
Number of pages11
JournalPhysical Review B-Condensed Matter
Issue number7
StatePublished - 1974
Externally publishedYes


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