一维轴次近邻伊辛模型中的奇异Yang-Lee边奇异性
Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model
摘要：
本文证明了外磁场中一维自旋为1/2的ANNNI（axial-next-to-nearest-neighbor-Ising）模型的Yang-Lee零点线密度在Yang-Lee边缘奇点处可能以临界指数$σ= -2/3$发散.这种不寻常行为的必要条件是转移矩阵特征值的三重退化。如果没有这个条件，我们就有通常的值$σ= -1/2$。在文献中，在自旋为1的Blume-Emery-Griffths模型和在具有两个复杂分量的磁场中的三态Potts模型中已经发现了类似的结果。我们的结果支持$σ= -2/3$的普遍性，它可能是一个一维足迹的三临界版本的杨李边缘奇点可能也存在于高维自旋模型。
英文摘要：
We show here for the one-dimensional spin-1/2 ANNNI (axial-next-to-nearest-neighbor-Ising) model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent $σ= -2/3$ at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer matrix eigenvalues. If this condition is absent we have the usual value $σ= -1/2$. Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of $σ= -2/3$ which might be a one-dimensional footprint of a tricritical version of the Yang-Lee-Edge singularity possibly present also in higher-dimensional spin models.
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