Critical Phase Transitions

Abstract

In this chapter, we first present the basic principles of a relatively new area of physics, the analysis of critical phase transitions and more generally the theory of criticality. Then, we will introduce some mathematical methods that set the physics of criticality on robust grounds.We will also discuss briefly some variation on the theme of criticality such as self-organized criticality, often used in theoretical approaches to biology. Following the current analyses in physics, we present them here as point-wise transitions, with respect to (usually) one control parameter. This will constitute an opening towards the approach to criticality in the following chapters seen as an “extended” phenomenon in biology, that, we propose, is ranging on a non-trivial interval of definition.