World Scientific Publishing Co. Pte. Ltd., 2004. – 302. – ISBN 981-238-583-5.It is hard to name another branch of physics more essentially changed in the last few decades than the theory of phase transitions. One can go further: having appeared in different variants of a mean field theory for the description of equilibrium phase transitions in problems of statistical physics and thermodynamics, the theory of phase transitions now appears to be an interdisciplinary science such as, say, the theory of oscillations. Also the concepts contained in the term “phase transition” has been substantially broadened. In condensed matter physics, besides traditional equilibrium thermodynamic phase transitions, this term includes quantum phase transitions, non-equilibrium dissipative phase transitions, percolation phenomena, etc.
During the last several decades we have witnessed intensive studies of the above phenomena in condensed matter physics, and of similar phenomena in different branches of physics (on a larger scale, of similar phenomena in chemistry, biology, ecology, economy). In particular, a breakthrough in understanding and precise quantitative description of the long-range properties of different systems in the vicinity of a second-order phase transition occured due to the applications of renormalization group ideas. Such an intensive and fruitful activity in the field sometimes leads to the opinion that all principal work in phase transitions theory had already been completed by the middle of the 80’s and no new physics remains to be explained. On the other hand, there exists an opposite opinion, stating that it is a fascinating part of physics still actively developing and there is a lot of work to be done in both the fundamental and the applied areas.
Contents of vol. 1
Mathematical Theory of the Ising Model and its Generalizations: an Introduction
Relaxation in Quantum Spin Chains: Free Fermionic Models
Quantum Phase Transitions in Alternating Transverse Ising Chains
Phase Transitions in Two-Dimensional Random Potts Models
Scaling of Miktoarm Star Polymers
Field Theoretic Approaches to the Superconducting Phase Transition
Contents of vol. 2
Introduction to the Non-Perturbative Renormalization Group
Introduction to Critical Dynamics
Spacetime Approach to Phase Transitions
Representations of Self-Organized Criticality
Phase Transitions in the Pseudospin-Electron Model
Contents of vol. 3
Universal Scaling Relations for Logarithmic-Correction Exponents
Phase Behaviour and Criticality in Primitive Models of Ionic Fluids
Monte Carlo Simulations in Statistical Physics — From Basic Principles to Advanced Applications
Ising Model on Connected Complex Networks
Minority Game: An “Ising Model” of Econophysics
