Lectures on Critical Phenomena

R. Brout

Somendra M. Bhattacharjee

Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of these phenomena and so, instead of following the traditional historical trail, we try to develop the subject in a way that emphasizes the length-scale based approach.

G. Toulouse

Somendra M. Bhattacharjee

Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of these phenomena and so, instead of following the traditional historical trail, we try to develop the subject in a way that lays stress on the length-scale based approach.

This book is the third volume of review papers on advanced problems of phase transitions and critical phenomena, following the success of the first two volumes in 2004 and in 2007. Broadly, the book aims to demonstrate that the phase transition theory, which experienced its 'golden age' during the 70s and 80s, is far from over and there is still a good deal of work to be done, both at the fundamental level and in respect of applications. This volume presents a broad spectrum of problems connected with criticality. It covers its theoretical backgrounds, analytical approaches and numerical simulations to describe criticality in specific systems (ionic fluids, diluted magnets, polymers), as well as phase transitions on complex networks and in the minority game model. As the first two volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the "Ising lectures" - a traditional annual workshop on phase transitions and critical phenomena which brings together scientists working in the field with university students and those who are interested in the subject.

David Paul Landau