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

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  • Fishman, Shmuel

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>.

Suggested Citation

  • Fishman, Shmuel, 1981. "Fourier space analysis of the Yvon-Born-Green equation in the critical region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(3), pages 382-402.
    • Handle: RePEc:eee:phsmap:v:109:y:1981:i:3:p:382-402
    DOI: 10.1016/0378-4371(81)90002-9
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    1. Baxter, Wt & Carrier, Nh, 1971. "Depreciation, Replacement Price, And Cost Of Capital," Journal of Accounting Research, Wiley Blackwell, vol. 9(2), pages 189-214.
    2. Kozak, David C., 1980. "Presidential Influence in Congress. By George C. EdwardsIII. (San Francisco: W. H. Freeman and Co., 1980. Pp. x + 216. $13.95, cloth; $6.95, paper.)," American Political Science Review, Cambridge University Press, vol. 74(4), pages 1079-1080, December.
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