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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 Percolation critical exponents ： ウィキペディア英語版 Percolation critical exponents In the context of percolation theory, a percolation transition is characterized by a set of ''universal'' critical exponents, which describe the fractal properties of the percolating medium at large scales and sufficiently close to the transition. The exponents are universal in the sense that they only depend on the type of percolation model and on the space dimension. They are expected not to depend on microscopic details like the lattice structure or whether site or bond percolation is considered. This article deals with the critical exponents of random percolation. Percolating systems have a parameter $p\backslash ,\backslash !$ which controls the occupancy of sites or bonds in the system. At a critical value $p\_c\backslash ,\backslash !$, the mean cluster size goes to infinity and the percolation transition takes place. As one approaches $p\_c\backslash ,\backslash !$, various quantities either diverge or go to a constant value by a power law in $|p\; -\; p\_c|\backslash ,\backslash !$, and the exponent of that power law is the critical exponent. While the exponent of that power law is generally the same on both sides of the threshold, the coefficient or "amplitude" is generally different, leading to a universal amplitude ratio. == Description == In the behavior of thermodynamic or configurational systems near a critical point or a continuous phase transition, the system become fractal and the behavior of many quantities are described by universal critical exponents. Percolation theory is a particularly simple and fundamental model in statistical mechanics which has a critical point, and a great deal of work has been done in finding its critical exponents, both theoretically (limited to two dimensions) and numerically. Critical exponents exist for a variety of observables, but most of them are linked to each other by exponent (or scaling) relations. Only a few of them are independent, and it is a matter of taste what the fundamental exponents are. One choice is the set $\backslash \backslash ,\backslash !$ motivated by the cluster size distribution, another choice is $\backslash \backslash ,\backslash !$ motivated by the structure of the infinite cluster. So-called correction exponents extend these sets, they refer to higher orders of the asymptotic expansion around the critical point. 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「Percolation critical exponents」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.