Z4-symmetric perturbations to the XY model from functional renormalization

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (Z4-symmetric) perturbations to the classical XY model in dimensionality d is an element of [2, 4]. In d = 3 we provide accurate estimates of the eigenvalue y4 corresponding to the leading irrelevant perturbation and follow the evolution of the physical picture upon reducing spatial dimensionality from d = 3 towards d = 2, where we approximately recover the onset of the Kosterlitz-Thouless physics. We analyze the interplay between the leading irrelevant eigenvalues related to O(2)-symmetric and Z4-symmetric perturbations and their approximate collapse for d -> 2. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.