The free energy singularity of the asymmetric six-vertex model and the excitations of the asymmetric XXZ chain
The free energy singularity of the asymmetric six-vertex model and the excitations of the asymmetric XXZ chain
复制标题
非对称六顶点模型的自由能奇点及非对称XXZ链的激励
DOI：
10.1016/s0550-3213(97)00078-3
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Birgit Wehefritz
中科院分区：
文献类型：
--
作者：
G. Albertini;S. Dahmen;Birgit Wehefritz
我们考虑了广泛用于描述晶体平衡形状的不对称六顶点模型和相应的不对称XXZ链。借助于Bethe-Anglesia解，我们确定了相边界上两个特殊点处的自由能奇异性，作为外场的函数。我们确认的指数3 - 2（检查实验，作为反铁电有序相是从通常的无公度相达到这个边界，我们确定了一个新的奇性沿着切向方向。两个奇点都描述了晶体在小平面附近的圆化。此时，自旋链的空穴激发在小动量下表现出色散关系ΔE <$N（ΔP）1 2，导致低激发态的有限尺寸标度ΔE <$N−1 2，N是链的尺寸。我们讨论了有序相的相变性质和Arrow-Arrow关联长度的行为。
We consider the asymmetric six-vertex model, widely used to describe the equilibrium shape of crystals, and the relevant asymmetric XXZ chain. By means of the Bethe-ansatz solution we determine the free energy singularity, as function of the external field, at two special points on the phase boundary. We confirm the exponent 3 2 (checked experimentally, as the antiferroelectric ordered phase is reached from the incommensurate phase normally to this boundary, and we determine a new singularity along the tangential direction. Both singularities describe the rounding off of the crystal near a facet. At this point the hole excitations of the spin chain show dispersion relations ΔE ∼ (ΔP)1 2at small momenta, leading to a finite-size scaling ΔE ∼ N−1 2 for the low-lying excited states, N being the chain size. We discuss the nature of the phase transition and the behavior of arrow-arrow correlation lengths in the ordered phase.