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 (Z_{4}-symmetric) perturbations to the classical XY model in dimensionality d∈[2,4]. In d=3 we provide accurate estimates of the eigenvalue y_{4} 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 Z_{4}-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.