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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Z N model ： ウィキペディア英語版 Z N model The $Z\_N$ model is a simplified statistical mechanical spin model. It is a generalization of the Ising model. Although it can be defined on an arbitrary graph, it is integrable only on one and two-dimensional lattices, in several special cases. == Definition == The $Z\_N$ model, sometimes known as the clock model, is defined by assigning a spin value at each node $r$ on a graph, with the spins taking values $s\_r=\backslash exp\}$, where $q\backslash in\; \backslash$. The spins therefore take values in the form of complex roots of unity. Roughly speaking, we can think of the spins assigned to each node of the $Z\_N$ model as pointing in any one of $N$ equidistant directions. The Boltzmann weights for a general edge $rr\text{'}$ are: ::$w\backslash left(r,r\text{'}\backslash right)=\backslash sum\_^x\_^\backslash left(s\_s\_^$ *\right)^k where $$ * denotes complex conjugation and the $x\_^$ are related to the interaction strength along the edge $rr\text{'}$. Note that $x\_^=x\_^$ and $x\_0$ is often set to 1. The (real valued) Boltzmann weights are invariant under the transformations $s\_r\; \backslash rightarrow\; \backslash omega^k\; s\_r$ and $s\_r\; \backslash rightarrow\; s^\_$, analogous to universal rotation and reflection respectively. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Z N model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.