The Theory of Critical Phenomena

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions areintroduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group andmean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.

“'The book is written very clearly and simply, which makes it accessible to anyone who passed the principal undergraduate physics courses ... Teachers and students either teaching or studying phase transitions ... should find this book very useful together with a number of additional sources... young researchers working in the area of phase transitions will benefit from the detailed description of the renormalization group theory.'Journal of Statistical Physics, Vol. 73, Nos 1/2, 1993”

'Provides a thorough introduction to the use of scaling and field-theoretic techniques that have become standard equipment in many areas of physics ... (jargon is kept to a minimum).'SciTech Book News, December 1992'A niche existed for a book in the important interface between the theory of critical phenomena and the technology of field theory ... it has now been most admirably filled by this volume ... interesting, readable and with very clear explanations and furthermore with excellent problems at the end of each chapter - all with complete solutions ... a book that can be unreservedly recommended to theoretical honours or starting graduate stuents; also toresearchers who may be seeking to fill a void in their understanding in this area.'VM.J. Buckingham, University of Western Australia, Australian & New Zealand Physicist, Volume 30, Number 12, December 1993`The book is written very clearly and simply, which makes it accessible to anyone who passed the principal undergraduate physics courses ... Teachers and students either teaching or studying phase transitions ... should find this book very useful together with a number of additional sources ... young researchers working in the area of phase transitions will benefit from the detailed description of the renormalization group theory.'Journal of Statistical Physics, Vol. 73, Nos 1/2, 1993

J. J. Binney is at Oxford University.

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.

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