论文标题
自旋相关功能，类似Ramus的身份以及约束晶格步行和平面分区的枚举
Spin correlation functions, Ramus-like identities, and enumeration of constrained lattice walks and plane partitions
论文作者
论文摘要
讨论了周期性海森堡XX链上翻转旋转的平均分布之间的关系与枚举组合学的某些方面之间的关系。 Bethe向量是该模型的国家向量，被认为是On-和offshell。正是这种方法使以非晶格步道和相关平面分区的非交流巢形式来表示和研究相关函数。我们区分两种类型的步行者，即锁定步骤模型和随机转弯。特别令人感兴趣的是随机转弯步行和循环矩阵的连接。具有对角部分固定高度的平面分区的标准生成函数的决定性表示，作为对Oft-Shell N颗粒伯特状态的产生指数的期望。生成指数的动力学平均值的渐近学以双缩放限制计算，前提是演变参数很大。结果表明，领先的渐近学的幅度取决于对角线约束平面分区的数量。
Relations between the mean values of distributions of flipped spins on periodic Heisenberg XX chain and some aspects of enumerative combinatorics are discussed. The Bethe vectors, which are the state-vectors of the model, are considered both as on- and off-shell. It is this approach that makes it possible to represent and to study the correlation functions in the form of non-intersecting nests of lattice walks and related plane partitions. We distinguish between two types of walkers, namely lock step models and random turns. Of particular interest is the connection of random turns walks and a circulant matrix. The determinantal representation for the norm-trace generating function of plane partitions with fixed height of diagonal parts is obtained as the expectation of the generating exponential over off-shell N-particle Bethe states. The asymptotics of the dynamical mean value of the generating exponential is calculated in the double scaling limit provided that the evolution parameter is large. It is shown that the amplitudes of the leading asymptotics depend on the number of diagonally constrained plane partitions.
