Criticality of the $O(2)$ model with cubic anisotropies from nonperturbative renormalization

Understand

We study the $O(2)$ model with $\mathbb{Z}_4$-symmetric perturbations within the framework of nonperturbative renormalization group (RG) for spatial dimensionality $d=2$ and $d=3$.

• In a unified framework we resolve the relatively complex crossover behavior emergent due to the presence of multiple RG fixed points.
• In $d=3$ the system is controlled by the $XY$, Ising, and low-$T$ fixed points in presence of a dangerously irrelevant anisotropy coupling $\lambda$.
• In $d=2$ the anisotropy coupling is marginal and the physical picture is governed by the interplay between two distinct lines of RG fixed points, giving rise to nonuniversal critical behavior; and an isolated Ising fixed point.