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

Understand

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.