翻訳と辞書 Words near each other ・ Spherical code ・ Spherical contact distribution function ・ Spherical coordinate system ・ Spherical cow ・ Spherical design ・ Spherical Earth ・ Spherical function ・ Spherical geometry ・ Spherical Harmonic ・ Spherical harmonic lighting ・ Spherical harmonics ・ Spherical image ・ Spherical law of cosines ・ Spherical mean ・ Spherical measure ・ Spherical model ・ Spherical multipole moments ・ Spherical neutron polarimetry ・ Spherical nucleic acid ・ Spherical Objects (band) ・ Spherical packing ・ Spherical pendulum ・ Spherical polyhedron ・ Spherical robot ・ Spherical roller bearing ・ Spherical roller thrust bearing ・ Spherical sector ・ Spherical segment ・ Spherical shell ・ Spherical space form conjecture Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spherical model ： ウィキペディア英語版 Spherical model The spherical model in statistical mechanics is a model of ferromagnetism similar to the Ising model, which was solved in 1952 by T. H. Berlin and M. Kac. It has the remarkable property that when applied to systems of dimension ''d'' greater than four, the critical exponents that govern the behaviour of the system near the critical point are independent of ''d'' and the geometry of the system. It is one of the few models of ferromagnetism that can be solved exactly in the presence of an external field. == Formulation == The model describes a set of particles on a lattice $\backslash mathbb$ containing ''N'' sites. For each site ''j'' of $\backslash mathbb$, a spin $\backslash sigma\_j$ which interacts only with its nearest neighbours and an external field ''H''. It differs from the Ising model in that the $\backslash sigma\_j$ are no longer restricted to $\backslash sigma\_j\; \backslash in\; \backslash$, but can take all real values, subject to the constraint that :$\backslash sum\_^N\; \backslash sigma\_j^2\; =\; N$ which in a homogeneous system ensures that the average of the square of any spin is one, as in the usual Ising model. The partition function generalizes from that of the Ising model to :$Z\_N\; =\; \backslash int\_^\; \backslash ldots\; \backslash int\_^\; d\backslash sigma\_1\; \backslash ldots\; d\backslash sigma\_N\; exp\; \backslash left(K\; \backslash sum\_\; \backslash sigma\_j\; \backslash sigma\_l\; +\; h\; \backslash sum\_j\; \backslash sigma\_j\; \backslash right)\; \backslash delta\; \backslash left(-\; \backslash sum\_j\; \backslash sigma\_j^2\; \backslash right)$ where $\backslash delta$ is the Dirac delta function, $\backslash langle\; jl\; \backslash rangle$ are the edges of the lattice, and $K=J/kT$ and $h=\; H/kT$, where ''T'' is the temperature of the system, ''k'' is Boltzmann's constant and ''J'' the coupling constant of the nearest-neighbour interactions. Berlin and Kac saw this as an approximation to the usual Ising model, arguing that the $\backslash sigma$-summation in the Ising model can be viewed as a sum over all corners of an ''N''-dimensional hypercube in $\backslash sigma$-space. The becomes an integration over the surface of a hypersphere passing through all such corners. It was rigorously proved by Kac and C. J. Thompson that the spherical model is a limiting case of the N-vector model. 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「Spherical 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.