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.

中文翻译：

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球面上XXZ铁磁模型的BKT跃迁

摘要 Berezinskii-Kosterlitz-Thouless (BKT) 跃迁是平面表面上的一种众所周知的现象。然而，对于弯曲的空间，情况并不清楚。在这项工作中，我们应用自洽谐波近似 (SCHA) 来研究球面上的 XXZ 铁磁模型。哈密​​顿量是根据规范共轭场（量子形式主义中的算子）S z 和 Φ 编写的，它们提供取决于温度的重整化自旋刚度。我们考虑了这个问题的半经典和量子方法。BKT 转变然后由提供自旋刚度突然消失的温度确定。我们的结果显示 T BKT 值接近于平面模型获得的值，并且它们与 BKT 相变理论的一般方面一致。