Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models

Alan D. Sokal, Andrei O. Starinets

    Research output: Contribution to journalArticle

    Abstract

    We compute the phase diagram in the N→∞ limit for lattice RPN-1, CPN-1 and QPN-1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

    Original languageEnglish (US)
    Pages (from-to)425-502
    Number of pages78
    JournalNuclear Physics, Section B
    Volume601
    Issue number3
    DOIs
    StatePublished - May 14 2001

    Fingerprint

    pathology
    phase diagrams
    hypergeometric functions
    partitions

    Keywords

    • Mixed isovector/isotensor model
    • Nematic liquid crystal* N→∞ limit* 1/N expansion
    • Nonlinear σ -model
    • RP model* CP model* QP model* N -vector model

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

    Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models. / Sokal, Alan D.; Starinets, Andrei O.

    In: Nuclear Physics, Section B, Vol. 601, No. 3, 14.05.2001, p. 425-502.

    Research output: Contribution to journalArticle

    Sokal, Alan D. ; Starinets, Andrei O. / Pathologies of the large- N limit for RPN-1 , CPN-1 , QPN-1 and mixed isovector/isotensor σ -models. In: Nuclear Physics, Section B. 2001 ; Vol. 601, No. 3. pp. 425-502.
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