Phase Transitions of the Second Order: Collective Variables Method Book

This book gives an original and up-to-date theory of the second order phase transitions based on the effective functional integral method. Unlike previous works, this theory is constructed ab initio, leading to a consistent description starting from the basic principles of statistical physics. The author introduces a new basic density measure, different from the Gaussian one, to describe the fluctuation in the system in the vicinity of the phase transition point. A new efficient method for partition function integration over the phase space layers is shown, as well as complete solutions of the recursion relations. For the first time, equations are found for the critical temperature and analytical calculations are accompanied by accurate numerical computations. The extensions of the theory for the cases of binary alloys and n-component Stanley model are considered and the collective variables representation for the cluster ferroelectric model are obtained. This modern theory of the phenomena at the second order phase transitions is a breakthrough in this area and would make an exceptionally valuable book for scientists, as well as an important textbook for postgraduates and undergraduates.