Fourier space analysis of the Yvon-Born-Green equation in the critical region

Details Fourier space analysis of the Yvon-Born-Green equation in the critical region Fourier space analysis of the Yvon-Born-Green equation in the critical region

Dec 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981phya..109..382f&link_type=abstract

Physica A, Volume 109, Issue 3, p. 382-402.

Astronomy and Astrophysics

Astronomy

9

Scientific paper

The pair correlation function implied by the Yvon-Born-Green (YBG) integral equation is analyzed in Fourier space in the critical region. For potentials of infinite range decaying like r-d-σ the upper borderline dimensionality above which the solutions can be Ornstein-Zernike-like is d> = 4 for σ >= 2 but d> = 2σ for σ < 2, while for finite range potentials d> = 4, confirming results found by real-space analysis. Although the borderline dimensionality is in agreement with expectations from lattice models and field theory, the analysis indicates that below d> the solutions of the YBG equation cannot exhibit a physically acceptable critical regime. Moreover, it is shown that corrections to the YBG equation arising from further terms in the BBGKY hierarchy diverge at criticality even for d>d>.
Present address: Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742, USA.

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