Critical Phenomena in Loop Models

"Critical Phenomena in Loop Models" is a specialized book that focuses on the application of loop models in physics, particularly in the context of continuous phase transitions. It provides a comprehensive analysis of the statistical properties of fluctuation loops and their relevance to various physical systems, such as polymer rings and quantum particles. The work is divided into two main parts: the first part examines three-dimensional loop ensembles and their relationship to line defects in disordered media, as well as to critical phenomena in two-dimensional quantum magnets. The second part is dedicated to novel two-dimensional loop models that go beyond traditional paradigms, presenting new insights into critical points and universal properties of polymer collapse transitions. These topics are explored in connection with sigma models on complex or real projective spaces, leading to an in-depth analysis of critical behavior in these field theories.