Stationary-point approach to the phase transition of the classical XY chain with power-law interactions.
Stationary-point approach to the phase transition of the classical XY chain with power-law interactions.
复制标题
具有幂律相互作用的经典 XY 链相变的驻点方法。
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Kastner
中科院分区：
文献类型：
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作者：
M. Kastner
分析了具有幂律对相互作用（即r{-α}随距离衰减的相互作用）的经典XY链的势能函数V的定定点。对于一类“自旋波型”平稳点，在大系统尺寸极限下，解析计算了V的Hessian行列式的渐近性质。计算是基于黑森的Toeplitz性质，并利用Szegö-type定理。这些结果有助于说明最近发现的相变与经典多体势稳态点性质之间的关系。根据这种关系，可以从指数α在0到1之间的Hessian行列式的行为中读出模型的确切相变势能。对于介于1和2之间的α，相变在行列式的行为中不表现出来，可能有必要考虑更大类别的驻点。
The stationary points of the potential energy function V of the classical XY chain with power-law pair interactions (i.e., interactions decaying like r{-α} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic behavior of the Hessian determinant of V is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szegö-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body potentials. In agreement with this relation, the exact phase transition potential energy of the model can be read off from the behavior of the Hessian determinant for exponents α between zero and one. For α between one and two, the phase transition is not manifest in the behavior of the determinant, and it might be necessary to consider larger classes of stationary points.
丙氨酸二肽的扩展谐波叠加方法和动力学的自由能表面
影响因子：
2.8
作者：
Strodel B
通讯作者：
Strodel B