Related Experiment Video
Updated: Apr 25, 2026

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
O(N)-universality classes and the Mermin-Wagner theorem
Alessandro Codello1, Giulio D'Odorico2
1SISSA, Via Bonomea 265, 34136 Trieste, Italy.
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.
Related Concept Videos
Second Uniqueness Theorem
In contrast, consider that the electric field is non-unique and apply Gauss's law in divergence form in the region between the conductors and the integral form to the surface...
Fundamental Theorem of Algebra
Norton's Theorem
Castigliano's Theorem
Thevinin's Theorem
Theorems of Pappus and Guldinus
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.

