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Solvable Models in Algebraic Statistical Mechanics (Science Research Papers): D.A. Dubin

The purpose of this book is to gather together the widely scattered material concerning some exactly solvable models of statistical-mechanical systems with an infinite number of degrees of freedom. By a process of selection and arrangement we hope that we have presented this material in a coherent and uniform setting.

It is assumed, but it is not necessary, that the reader is acquainted with the physical motivation behind the models discussed, for our analysis of such matters is necessarily brief (Boltzmann [1,2]; Born [1]; Ehrenfest and Ehrenfest [1]; Gibbs [1]; Guggenheim [1]; Huang [1]; Landau and Lifschitz [1]; London [1]; Mattis ;Schrodinger [1]).

We have also assumed a concurrent - or prior - knowledge of the pertinent material in the textbooks of Emch [1] and Rue lie [1]. Another good reference is the text of Eckmann and Guenin [1]. Any supplementary mathematics required of the reader will be found in the various textbooks referred to in the body of this text.

The readers we had in mind during the writing were, primarily, graduate students embarking on research projects in statistical mechanics. In addition, it is hoped that this book will be of use to the general community of research workers in statistical mechanics and applied mathematics.

With this in mind, in spite of the rather technical nature of the material, very few detailed proofs are presented. Most statements and theorems are proven 'by reference', generally to a journal article. For it is not expected that the reader we had in mind will wish to know all such details, particularly at first reading. If we have managed to convey the general flavour of the subject and enough background to enable the reader to find his way through the literature, then we shall have achieved our aim.

A book such as this is almost surely plagued with errors; but I am not the first author to be faced with this problem. Concerning his dictionary (Johnson, S. A755). A dictionary of the English language), Samuel Johnson defended his authorship thus: '. . . a few wild blunders and risible absurdities, from which no work of such multiplicity was ever free, may for a time furnish folly with laughter .. . What is obvious is not always known, and what is known is not always present. In this work, when it shall be found that much is omitted, let it not be forgotten that much is likewise performed.

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