海森堡铁磁体的量子稳定性
Quantum Stability for the Heisenberg Ferromagnet
摘要：
RxS ^[3]上的高自旋经典弦可以用朗道-利夫希茨模型来描述，或者等价地用热力学极限下的海森堡铁磁体来描述。该模型的谱可用谱曲线的形式给出。然而，这是一个先验不清楚是否任何给定的容许谱曲线实际上可以实现为一个解决方案的离散贝特方程，一个属性，可以被称为稳定性。为了研究稳定性问题，我们寻找并探讨了一般的两截解或椭圆曲线。事实证明，这条椭圆曲线的模空间显示出令人惊讶的丰富结构。我们提出了各种情况下的插图，从而获得一些洞察多切割解决方案的特点。看来，所有可容许的谱曲线确实是稳定的，如果分支切割被定位在一个合适的，非平凡的方式。
英文摘要：
Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it is a priori not clear whether any given admissible spectral curve can actually be realised as a solution to the discrete Bethe equations, a property which can be referred to as stability. In order to study the issue of stability, we find and explore the general two-cut solution or elliptic curve. It turns out that the moduli space of this elliptic curve shows a surprisingly rich structure. We present the various cases with illustrations and thus gain some insight into the features of multi-cut solutions. It appears that all admissible spectral curves are indeed stable if the branch cuts are positioned in a suitable, non-trivial fashion.
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