论文标题
与非本地耦合的自洽谐波近似
Self-consistent harmonic approximation with non-local couplings
论文作者
论文摘要
我们得出了具有非本地交互的$ 2D $ XY模型的自洽谐波近似。各种形式的自旋旋转耦合以及任何尺寸的差异耦合的结果方程都保留。然后，我们的分析专门针对距离$ r $ as $ \ propto 1/r^{2+σ} $腐烂的幂律耦合，以调查berezinskii-kosterlitz的有限$σ$的鲁棒性，该$σ$在短范围内发生在短范围内的$ c $ fty $ c。我们为变异耦合的功能形式提出了一个ANSATZ，并表明，对于任何$σ> 2 $，BKT机构都会发生。本研究为下部临界阈值$σ^\ ast = 2 $提供了上限，尽管LR耦合，但传统的BKT过渡仍然存在。
We derive the self-consistent harmonic approximation for the $2D$ XY model with non-local interactions. The resulting equation for the variational couplings holds for any form of the spin-spin coupling as well as for any dimension. Our analysis is then specialized to power-law couplings decaying with the distance $r$ as $\propto 1/r^{2+σ}$ in order to investigate the robustness, at finite $σ$, of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which occurs in the short-range limit $σ\to \infty$. We propose an ansatz for the functional form of the variational couplings and show that for any $σ>2$ the BKT mechanism occurs. The present investigation provides an upper bound for the lower critical threshold $σ^\ast=2$, above which the traditional BKT transition persists in spite of the LR couplings.
