Continuum limits and exact finite-size-scaling functions for one-dimensional O(N)-invariant spin models

Attilio Cucchieri, Tereza Mendes, Andrea Pelissetto, Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We solve exactly the general one-dimensional O(N)-invariant spin model taking values in the sphere SN - 1, with nearest-neighbor interactions, in finite volume with periodic boundary conditions, by an expansion in hyperspherical harmonics. The possible continuum limits are discussed for a general one-parameter family of interactions and an infinite number of universality classes is found. For these classes we compute the finite-size-scaling functions and the leading corrections to finite-size scaling. A special two-parameter family of interactions (which includes the mixed isovector/isotensor model) is also treated and no additional universality classes appear. In the appendices we give new formulae for the Clebsch-Gordan coefficients and 6-j symbols of the O(N) group, and some new generalizations of the Poisson summation formula; these may be of independent interest.

    Original languageEnglish (US)
    Pages (from-to)581-673
    Number of pages93
    JournalJournal of Statistical Physics
    Volume86
    Issue number3-4
    DOIs
    StatePublished - Feb 1997

    Keywords

    • Continuum limit
    • Finite-size scaling
    • Hyperspherical harmonics
    • Mixed isovector/isotensor model
    • N-vector model
    • One-dimensional
    • RP model
    • Universality classes
    • σ-model

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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