论文标题
海森贝格XX链，非合并的参数化产生指数和对角线限制的平面分区
Heisenberg XX chain, non-homogeneously parameterised generating exponential, and diagonally restricted plane partitions
论文作者
论文摘要
获得并研究了周期性的海森贝格XX模型的非均匀参数化产生指数的平均值。具有固定体积的对角线零件的盒装平面分区的标准生成函数，作为生成指数的N颗粒平均值。自避免随机转弯步行的生成函数是根据导致Ramus身份概括的循环矩阵获得的。在生成指数的各种规格下，对于一组不对不的翻转旋转以及第一瞬间的旋转旋转分布的力量，N粒子平均会产生。这些平均值是通过封闭轨迹的数量来表示的，并具有约束的初始/最终位置。大时间参数的估计值是通过对角线限制的平面分区的数量表示的，这些平面分区的特征是主对角线迹线的固定值或对角线柱的固定高度，以与翻转旋转位置的一对一对应关系。
The mean values of non-homogeneously parameterized generating exponential are obtained and investigated for the periodic Heisenberg XX model. The norm-trace generating function of boxed plane partitions with fixed volume of their diagonal parts is obtained as N-particles average of the generating exponential. The generating function of self-avoiding walks of random turns vicious walkers is obtained in terms of the circulant matrices that leads to generalizations of the Ramus's identity. Under various specifications of the generating exponential, the N-particles averages arise for a set of inconsecutive flipped spins and for powers of the first moment of flipped spins distribution at large length of the chain. These averages are expressed through the numbers of closed trajectories with constrained initial/final positions. The estimates at large temporal parameter are expressed through the numbers of diagonally restricted plane partitions characterized by fixed values of the main diagonal trace or by fixed heights of the diagonal columns in one-to-one correspondence with the flipped spins positions.
