论文标题
由置换复杂度度量激励的具有置换式旋转的Ising模型
An Ising model having permutation spin motivated by a permutation complexity measure
论文作者
论文摘要
在本文中，我们定义了ISING模型的变体，其中旋转被排列替换。两个自旋之间的能量是另一个自旋的相对障碍的函数。该模型是由声明性系统的复杂度度量的动机。对于这样的系统，状态是置换，置换分类复杂性测量邻近状态的平均顺序疾病。为了测量两个旋转之间的相对混乱，我们使用了在Chatterjee \＆Diaconis和Petersen的作品中出现的下降置换统计统计量的对称版本。经典的ISING模型对应于该新模型的长度-2置换案例。我们考虑并证明了该模型的1D情况的某些基本特性，其中旋转为长度3置换量。
In this paper we define a variant of the Ising model in which spins are replaced with permutations. The energy between two spins is a function of the relative disorder of one spin, a permutation, to the other. This model is motivated by a complexity measure for declarative systems. For such systems a state is a permutation and the permutation sorting complexity measures the average sequential disorder of neighbouring states. To measure the relative disorder between two spins we use a symmetrized version of the descent permutation statistic that has appeared in the works of Chatterjee \& Diaconis and Petersen. The classical Ising model corresponds to the length-2 permutation case of this new model. We consider and prove some elementary properties for the 1D case of this model in which spins are length-3 permutations.
