Order, Disorder and Criticality: Advanced Problems of Phase Transition Theory

This work reviews some topics in the theory of phase transitions and critical phenomena. They include: mathematical theory of the Ising model; equilibrium and non-equilibrium criticality of one-dimensional quantum spin chains; influence of structural disorder on the critical behaviour of the Potts model; p-criticality, fractality and multifractality of linked polymers; field-theoretical approaches to the superconducting phase transitions; phase transitions in strongly correlated electron systems. The book is based on review lectures that were given at an annual seminar ("The Ising Lectures") which aims at promoting and deepening the study of critical phenomena as well as exchanging information between scholars and students.