1999
DOI: 10.1590/s0103-97331999000300025
|View full text |Cite
|
Sign up to set email alerts
|

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 nite size scaling hypothesis, the approximate critical behavior of model on in nite lattice is obtained through the exact computation of some thermal quantities of the model on nite clusters. In this work some of these methods are reviewed, namely the mean eld renormalization group, the e ective eld renormalization group and th… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
55
1

Year Published

2000
2000
2024
2024

Publication Types

Select...
7
1

Relationship

0
8

Authors

Journals

citations
Cited by 48 publications
(56 citation statements)
references
References 181 publications
(264 reference statements)
0
55
1
Order By: Relevance
“…In this paper, we apply the mean field RG (MFRG) method [16,17] to treat the critical properties of the anisotropic XY model on a semi-infinite lattice. The MFRG approach is based on the comparison of two clusters of different sizes, each of them simulating the infinite system.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…In this paper, we apply the mean field RG (MFRG) method [16,17] to treat the critical properties of the anisotropic XY model on a semi-infinite lattice. The MFRG approach is based on the comparison of two clusters of different sizes, each of them simulating the infinite system.…”
Section: Methodsmentioning
confidence: 99%
“…(6), (8) and (10) for the one-spin cluster with Eqs. (7), (9) and (11) for the two-spin cluster with the MFRG ideas [16,17] we obtain the following set of equations:…”
Section: And the Corresponding Symmetry Breaking Fieldsmentioning
confidence: 99%
“…This method was proposed some time ago [11] and has been successfully applied to classical systems (both static and dynamic properties have been studied), like Ising, Potts, or BlumeCapel models [12]. The second is just the generalization of the usual bond-moving Migdal-Kadanoff [13] approximation to antiferromagnetic quantum systems.…”
Section: Formalismmentioning
confidence: 99%
“…The Fe 1−q Al q system in the bcc structure shows an interesting magnetic behavior since its critical temperature decreases with q = 1 − c but shows a kind of plateau for low Al concentrations. Theoretical studies [5,6], using mean field renormalization group [7] and Bogoliubov inequality [8] approaches have been used to explain this behavior by taking a simple Ising Hamiltonian. Sato and Arrot [9] obtained the magnetization by assuming a ferromagnetic exchange between nearest-neighbor Fe atoms and an antiferromagnetic superexchange between two Fe atoms separated by an Al atom.…”
Section: Introductionmentioning
confidence: 99%