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arXiv · 1210.4037

O(N)-Universality Classes and the Mermin-Wagner Theorem

A. Codello·G. D'Odorico
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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 fractal dimension in the range 2<d<3 we observe, for any N bigger than or equal to 1, a finite family of multi-critical effective potentials of increasing order. Apart for 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.

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A. Codello, G. D'Odorico. 2012-10-15. O(N)-Universality Classes and the Mermin-Wagner Theorem. https://doi.org/10.1103/physrevlett.110.141601

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