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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 Ising critical exponents ： ウィキペディア英語版 Ising critical exponents This article lists the critical exponents of the ferromagnetic transition in the Ising model. In statistical physics, the Ising model describes a continuous phase transition with scalar order parameter. The critical exponents of the transition are universal values and characterise the singular properties of physical quantities. The ferromagnetic transition of the Ising model establishes an important universality class, which contains a variety of phase transitions as different as ferromagnetism close to the Curie point and critical opalescence of liquid near its critical point. From the quantum field theory point of view, the critical exponents can be expressed in terms of scaling dimensions of the local operators $\backslash sigma,\backslash epsilon,\backslash epsilon\text{'}$ of the conformal field theory describing the phase transition (In the Ginzburg-Landau description, these are the operators normally called $\backslash phi,\backslash phi^2,\backslash phi^4$.) These expressions are given in the last column of the above table, and were used to calculate the values of the critical exponents using the operator dimensions values from the following table: In d=2, the conformal field theory in question is the minimal model $M\_$. In d=4, it is the free massless scalar theory (also referred to as mean-field theory). These two theories are exactly solved, and the exact solutions give values reported in the table. The d=3 theory is not yet exactly solved. This theory has been traditionally studied by the renormalization group methods and Monte-Carlo simulations. The estimates following from those techniques, as well as references to the original works, can be found in Refs. and.〔Kleinert, H., ("Critical exponents from seven-loop strong-coupling φ4 theory in three dimensions". )Physical Review D 60, 085001 (1999)〕 More recently, a conformal field theory method known as the conformal bootstrap has been applied to the d=3 theory.〔〔 This method gives results in agreement with the older techniques, but an order of magnitude more precise. These are the values reported in the table. More information on critical exponents may be found at (SklogWiki ) == References == 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「Ising 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.