Download PDF by Elliott H. Lieb: Mathematical Physics in One Dimension. Exactly Soluble

Download PDF by Elliott H. Lieb: Mathematical Physics in One Dimension. Exactly Soluble

By Elliott H. Lieb

''why are nontrivial types of actual structures so usually soluble in a single measurement yet now not in 3 dimensions''

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Extra resources for Mathematical Physics in One Dimension. Exactly Soluble Models of Interacting Particles

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Sur un tel intervalle, α doit rester constant quand / varie; d'après ( 3 . 6 ) , la dérivée dg(a)/da doit donc présenter une discontinuité. Nous allons voir que cette circonstance est impossible. 4) sont les zéros d'une fonction entière D (λ). On ia) s'assure facilement que pour Re (a) > 0, la fonction D (λ) est simultanément holomorphe en a et λ. Comme le noyau de l'équation e (a) est positif, il résulte d'un théorème de J e n t ζ s c h ) que D (λ) a une racine de valeur absolue minimum, à la fois unique, simple et (α) (a) {α) réelle.

8) E . G ο u r s a t, Cours d'Analyse Mathématique, vol. I I I , Paris, 1927, chap. X X X I . 34 M A T H E M A T I C A L P H Y S I C S IN ONE DIMENSION Τ 11 Κ J O U R N A L OF Cil RM IC A L PHYSICS V Ο ΜΙ M Κ 2 1. N U M Β K R 6 JUNK. I 9$ 3 Molecular Distribution Functions in a One-Dimensional Fluid* Ζκνι W . SALSBURG, KOBKRT W . ZWANZIG, AND JOHN G . KIRKWOOD Sterling Chemistry iMboralory, Yale University^ New Haven, Connecitut (Received February 4, 1 9 5 3 ) Exact expressions are derived for the molecular distribution functions in a one-dimensional fluid whose particles interact with a nearest neighbor pair potential.

2. L I M I T O F L O N G - R A N G E F O R C E S N We shall illustrate a more general result on the behavior of various order-disorder models by three examples : the Gaussian model, the spherical model, and the Ising model. For these three models (and in fact for a whole class of models) the partition function is the same above the critical point through terms of order 1/R, where R is the range of the force. Below the transition point there is little or no relationship. We shall ; N A FF NU O Q NT N £P TE T I R OTM E HI S M U O R Y U AE ^ F O the system to be performed easily.

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