Phenomenological Renormalization Group Methods

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.

Review Article

Cited by in corpus (13)

• Percolation on two- and three-dimensional lattices
• Reals-space renormalization group study of the anisotropic antiferromagnetic Heisenberg model on the square lattice
• Phase Diagram and Critical Behavior of the Spin-1 Baxter-Wu Model with a Crystal Field
• Critical behavior of 2 and 3 dimensional ferro- and antiferromagnetic spin ice systems in the framework of the Effective Field Renormalization Group technique
• The anisotropic Ashkin-Teller model: a renormalization group study
• Random Sampling Neural Network for Quantum Many-Body Problems
• A New Approach to Real Space Renormalization Group Treatment of Ising Model for Square and Simple Cubic Lattice
• Phase diagram of the Kondo necklace: a mean-field renormalization group approach
• Universality in the partially anisotropic three-dimensional Ising lattice
• Phase transition induced for external field in tree-dimensional isotropic Heisenberg antiferromagnet
• Revisiting the one-dimensional diffusive contact process
• Exact relations between damage spreading and thermodynamic functions for the N-color Ashkin-Teller model
• Magnetic Behaviour of Disordered Ising Ferrimagnet in High Magnetic Field