title: O(N)-universality classes and the Mermin-Wagner theorem.
abstract: We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the Mermin-Wagner-Hohenberg theorem set in as we gradually deform theory space towards d = 2. For a fractal dimension in the range 2 < d < 3, we find, for any N ≥ 1, a finite family of multicritical effective potentials of increasing order. Apart from the N = 1 case, these disappear in d = 2 consistently with the Mermin-Wagner-Hohenberg theorem. Finally, we study O(N = 0)-universality classes and find an infinite family of these in two dimensions.
authors.affiliation: SISSA, Via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Codello
authors.affiliation: SISSA, Via Bonomea 265, 34136 Trieste, Italy and INFN, Sezione di Trieste, Via Bonomea 265, 34136 Trieste, Italy.
authors.forename: Giulio
authors.initials: G
authors.lastname: D'Odorico