${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization

Abstract

We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic (${\mathbb{Z}}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. 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 ${\mathbb{Z}}_4$-symmetric perturbations and their approximate collapse for $d\to 2$. We compare and discuss different implementations of the derivative expansion in cases involving one and two invariants of the corresponding symmetry group.

14 pages, 7 figures

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Cited by in corpus (2)

• The $q-$state Potts model from the Nonperturbative Renormalization Group
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