Phenomenological Renormalization Group Methods

TL;DR

This paper reviews phenomenological renormalization group methods, focusing on their theoretical foundations, applications, and interrelations, highlighting the mean field approach's versatility in studying various systems.

Contribution

It provides a comprehensive review of several phenomenological RG methods, emphasizing the mean field renormalization group and discussing their potential and connections.

Findings

Mean field renormalization group is widely applied to diverse systems.

Finite size scaling techniques help approximate critical behavior.

Interrelations among different RG methods are explored.

Abstract

Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate critical behavior of the model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more applied an extended to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also addressed.