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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 Replica trick ： ウィキペディア英語版 Replica trick In statistical physics of spin glasses and other systems with quenched disorder, the replica trick is a mathematical technique based on the application of the formula : $\backslash lim\_\; =\backslash ln\; Z.$ == Mathematical Trick == This mathematical trick is used in computation involving functions of a variable that can be expressed as a power series in that variable. The crux of this technique is to reduce the function of a variable, say $f(z)$, into powers of $z$ or, in other words, replicas of $z$, and perform the same computation which is to be done on $f(z)$, using the powers of $z$. A particular case which is of great use in physics is in averaging the free energy, or $-\backslash ln\; Z()$, over values of $J\_$ with a certain probability distribution, typically Gaussian, and the function $Z()\; \backslash sim\; e^"\; TITLE="J\_">)$(or more generally, any power of $J\_$) and not its logarithm which we wanted to average, the resulting integral (assuming a Gaussian distribution) would be of the form $\backslash int\; dJ\_\; e^\; =\; \backslash lim\_\backslash dfrac$ which clearly reduces the task of averaging to solving a relatively simpler Gaussian integral. The replica trick involves extending this argument to the case where $n$ is no longer constrained to be an integer, by positing that if $Z^n$ can be calculated for all positive integers $n$ then this may be sufficient to allow the limiting behaviour as $n\backslash to0$ to be calculated. Clearly, such an argument poses many mathematical questions, and the resulting formalism for performing the limit $n\backslash to0$ typically introduces many subtleties (see Mezard et al.). When using mean field theory to perform one's calculations, taking this limit often requires introducing extra order parameters, in consequence of 'replica symmetry breaking' which is closely related to ergodicity breaking and slow dynamics within disorder systems. 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「Replica trick」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.