BKT transition of the XXZ ferromagnetic model on the spherical surface

Abstract The Berezinskii-Kosterlitz-Thouless (BKT) transition is a well-known phenomenon on planar surfaces; however, for curved spaces, the situation is not clear. In this work, we applied the Self-consistent Harmonic Approximation (SCHA) to study the XXZ ferromagnetic model on the spherical surface. The Hamiltonian is written in terms of the canonically conjugate fields (operators in the quantum formalism) S z and Φ that provide a renormalized spin stiffness depending on temperature. We consider both semiclassical and quantum approaches to the problem. The BKT transition is then determined by the temperature that provides abrupt vanishing of the spin stiffness. Our results show T BKT values close to that obtained for the planar model, and they are in agreement with the general aspects of the BKT phase transition theory.