The relationship between liquids and gases engaged the attention of a number of distinguished scientists in the mid 19th Century. In a definitive paper published in 1869, Thomas Andrews described experiments he performed on carbon dioxide and from which he concluded that a critical temperature exists below which liquids and gases are distinct phases of matter, but above which they merge into a single fluid phase. During the years which followed, other natural phenomena were discovered to which the same critical point description can be applied - such as ferromagnetism and solutions. This book provides an historical account of theoretical explanations of critical phenomena which ultimately led to a major triumph of statistical mechanics in the 20th Century - with the award of the Nobel Prize for Physics
Table of Contents
1. Preface 2. Historical Survey 3. Fluids: Classical Theory 4. Light Scattering and Correlations: Classical Theory 5. The Onsager Revolution 6. Reconciliation 7. Renormalization Group 8. Appendix: Related Topics 9. References 10. Index
Foreword: About the Author and the Subject
1 Historical Survey
1.1 The Development of Statistical Mechanics
1.2 Gibbs Ensembles
1.3 Non-interacting and Interacting Systems
1.4 The Classical Period
1.5 The Onsager Revolution
1.7 Renormalization Group: Respectability
2 Fluids: Classical Theory
2.1 Thermodynamic Background
2.2 Stability of a Phase: First-order Transitions
2.3 Theory of van der Waals
2.4 Critical Behaviour of a van der Waals Fluid (T > Tc)
2.5 Critical Behaviour of a van der Waals Fluid (T
"… a book by a world authority and true pioneer who was there in the earliest days of the revolutionary developments that he describes, that he himself helped launch and then continued to guide.
This is the dramatic story that Cyril Domb lived through and thought through: he tells it here, for the student and non-specialist reader, with the practiced hand of a devoted and experienced scholar and teacher.
As a teacher and expositor, Cyril Domb brought new horizons and opportunities to his students and provided them with the tools and ideas to forge ahead. This book will surely do the same for those new to the field or for those wishing to revive or extend their acquaintance with it.
"An Appendix to this book points to some of those further directions: in particular, to percolation phenomena and macromolecular solutions, in which the author's pioneering work set the stage for significant modern advances."
-- Michael Fisher, distinguished University Professor, and Regents Professor in the University of Maryland, from the Introduction
"This revolution is the topic of Cyril Domb's lovely monograph The Critical Point, based on graduate lectures he has given over the years, first at London University and, more recently, at Israel's Bar-Ilan University, where he now works. The fact that Domb was also an important participant in the events he describes gives his historical account a special immediacy.
"The exposition throughout is admirably balanced, introducing along the way important techniques and approaches (including series expansions) in an understandable manner, without dwelling unduly on technical details. An excellent set of references is supplied with each chapter.
"The Critical Point is a friendly and very personal overview and testament, clearly intended for students and colleagues. As Michael Fisher - one who falls into both of these categories - writes in a gracefully appreciative forward, "One could not wish for a more expert and sympathetic guide to introduce one to a major triumph of theoretical and experimental science in our century."
-- Michael Wortis in Physics Today, December 1997
"It is the story of the confluence of these two streams and of the remarkable advances in the science of condensed matter to which it led that Cyril Domb tells in his wonderful book "The Critical Point".
"It is a lively and authoritative account of the history and present state of our understanding of equilibrium critical-point phenomena.
"The Critical Point" by Cyril Domb is going to be and is going long to remain a definitive reference work on the statistical mechanics of critical phenomena. It is scholarship of the highest order."
-- Ben Widom in Bulletin de la Society de Physique Francaise in 1997, translated in January 1998
"The book is subtitled: "A historical introduction to the modern theory of critical phenomena." Indeed the book is deliberately written to include the actors and not just the final polished outcomes, and it is quite unique in this.
"The book would be well worth reading just for the historical record, and as a nice case study of the development of scientific thought. However, it is much more than that.
"The book could provide material for an Honours course, covering a selection of topics, or for a graduate course either given formally or through prescribed reading."
-- J. Oitmaa in Physics in Australia, 1997
" Overall, his treatment is authoritative, his coverage comprehensive, and his awareness of the sensitivity to readers is exemplary.
Domb is to be congratulated on his lightness of touch in an area that could easily be quite heavy going. I predict that this book will be a classic in its field for many years to come.
-- Chemistry in Britain, 1997
"… he presents a lucid, comprehensive review of an important area of modern physics, and he tells the fascinating story of how our present understanding of this subject was achieved. He succeeds in making these two undertakings reinforce rather than conflict with each other; the historical approach makes the physics and mathematics easier to comprehend, and the technical material provides depth and substance to the historical account.
"Anyone interested in statistical mechanics and critical phenomena will find much to enjoy in this book, from the clear analysis of scientific strategy to the personal recollections of decisive events, presented with enthusiasm and style by one who played an important role in the story. I would recommend it especially for graduate students in all areas of physics for enlightenment and for inspiration."
-- Stephen Brush in Notes and Records, Royal Soc. London, 52, 1998
"…Domb gives superb account of all three phases of his subject - the classical (90 pages), Onsager (130 pages), and the renormalization group (100 pages). He writes with the authority of one who has read widely in the early history, who contributed substantially, with his research group at King's College, London, to the working out of what he calls the 'Onsager revolution'."
-- J. S. Rowlinson (a Vice President of the Royal Society) in Journal of Statistical Physics, 1997