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

Shmuel Fishman

Physica A: Statistical Mechanics and its Applications, 1981, vol. 109, issue 3, 382-402

Abstract: 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>.

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:109:y:1981:i:3:p:382-402

DOI: 10.1016/0378-4371(81)90002-9

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