## Abstract

We solve exactly the general one-dimensional O(N)-invariant spin model taking values in the sphere S^{N - 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 language | English (US) |
---|---|

Pages (from-to) | 581-673 |

Number of pages | 93 |

Journal | Journal of Statistical Physics |

Volume | 86 |

Issue number | 3-4 |

DOIs | |

State | Published - 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