There are now quite a number of books available on the theory of critical phenomena. Does the world really need another? We believe this book does fill a gap in the literature for several reasons.

First, it combines discussions of exact solutions, numerical simulations, real-space renormalization and field-theoretic methods, in a way which we hope illuminates the similarities and differences, and the strengths and weak- nesses, of all these approaches to the study of continuous phase transitions. Second, we have tried hard to make the book accessible to students with a good undergraduate background in physics but no knowledge of quantum field theory. Thus, we have taken pains to exclude as much jargon as possible, and to define clearly those technical terms that we do require. We have also tried to make the book as self-contained as possible by covering in boxes and appendices the technical details and mathematical techniques which are necessary for the solution of some of the more difficult problems in the field, but with which the reader may be unfamiliar.

Finally, at the end of each chapter we give several problems, which we hope will help readers to become familiar with the concepts and techniques introduced in that chapter. Complete solutions to all the problems are given at the back of the book.

While writing this book we have drawn freely on many sources, but es- pecially on the books by Daniel Amit (1984), Shang-Keng Ma (1976), Gior- gio Parisi (1988), Eugene Stanley (1971), and Jean Zinn-Justin (1989). In addition we are indebted to many people for helpful comments and suggestions, and for interesting conversations and seminars on the subject of critical phenomena. We would in particular like to thank Eytan Domany for the outstanding series of lectures he gave at Oxford in 1991, and Rob Phillips, Bruce Roberts and Jan von Delft for their careful reading of the manuscript and many helpful criticisms. Thanks are also due to Lawrence Harwood and the Dyson Perrins Laboratory for making Figure 1.8 possible.

Oxford January 1992



Answers 429

References 448

Index 453