IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v109y1981i3p382-402.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437181900029
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(81)90002-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Baxter, Wt & Carrier, Nh, 1971. "Depreciation, Replacement Price, And Cost Of Capital," Journal of Accounting Research, Wiley Blackwell, vol. 9(2), pages 189-214.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fishman, Shmuel & Fisher, Michael E., 1981. "Critical point scaling in the Percus-Yevick equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(1), pages 1-13.
    2. den Hollander, W.Th.F. & Kasteleyn, P.W., 1982. "Random walks with ‘spontaneous emission’ on lattices with periodically distributed imperfect traps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(3), pages 523-543.
    3. Lekkerkerker, H.N.W., 1997. "Strong, weak and metastable liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 244(1), pages 227-237.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:109:y:1981:i:3:p:382-402. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.