1995/09/11 by Attilio Cucchieri, Tereza Mendes, Andrea Pelissetto +1 · 18 citations
Mathematics · Physics and Astronomy · #Geometry #Invariant (physics) #Mathematical physics #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Random Matrices and Applications #Scale invariance #Scaling #Statistical physics #Theoretical and Computational Physics #hep-lat
paper · pdf · doi:10.1007/bf02199114
published in Journal of Statistical Physics 86(3-4), 581-673 (Springer Science+Business Media) · 541038 bytes uuencoded gzip'ed (expands to 1301207 bytes Postscript); 88 pages including all figures
arxiv created 1995/09/11 · openalex publication_date 1997/02/01 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.