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    Renormalisation group flow and geodesics in the O(N) model for large N


    Dolan, Brian P. (1998) Renormalisation group flow and geodesics in the O(N) model for large N. Nuclear Physics B, 528 (3). pp. 553-576. ISSN 0550-3213

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    Abstract

    A metric is introduced on the space of parameters (couplings) describing the large N limit of the O(N) model in Euclidean space. The geometry associated with this metric is analysed in the particular case of the infinite volume limit in three dimensions and it is shown that the Ricci curvature diverges at the ultra-violet (Gaussian) fixed point but is finite and tends to constant negative curvature at the infra-red (Wilson-Fisher) fixed point. The renormalisation group flow is examined in terms of geodesics of the metric. The critical line of cross-over from the Wilson-Fisher fixed point to the Gaussian fixed point is shown to be a geodesic but all other renormalisation group trajectories, which are repulsed from the Gaussian fixed point in the ultraviolet, are not geodesics. The geodesic flow is interpreted in terms of a maximisation principle for the relative entropy.

    Item Type: Article
    Keywords: Renormalisation group; Cross-over; Entropy; Spherical model; Geodesic;
    Academic Unit: Faculty of Science and Engineering > Mathematical Physics
    Item ID: 10498
    Identification Number: https://doi.org/10.1016/S0550-3213(98)00457-X
    Depositing User: IR Editor
    Date Deposited: 18 Feb 2019 14:46
    Journal or Publication Title: Nuclear Physics B
    Publisher: Elsevier
    Refereed: Yes
    URI:

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