Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

Improved mean-field-like renormalisation group approach for Z(q) symmetric spin models

Ernst Niebur, Jenő Sólyom

Published Jan 21, 1988• 3 citations
Publisher

Abstract

Various modifications of the mean-field renormalisation group method are analysed to study the convergence of the critical coupling and critical exponents to their exact values as the cluster size increases. Appropriate choice of the length scaling factor or of the scaling quantity can give appreciable improvement over the conventional procedure for short clusters. The best values are achieved when both the bulk and surface critical behaviour are explicitly taken into account.

DOI
10.1088/0305-4470/21/2/031

Related papers

Mean-field-like variational and renormalisation group studies of (1+1)-dimensional spin models

Ernst Niebur, Jenő Sólyom

Two recently proposed methods, the variational cluster wavefunction approximation and the mean-field-like renormalisation group transformation, are used to describe the phase transitions in the Hamiltonian version of the two-dimensional Z(q) symmetric spin models. The convergence of the two schemes to the known results is analysed. It is shown that in their usual form neither of these models can reproduce fine details of the phase diagram, although the renormalisation group method gives in general better convergence.

Journal of Physics A Mathematical and General•Jul 11, 1987•1 citation

Two-step renormalisation group for Ising systems

O. F. de Alcantara Bonfim, F. C. Sá Barreto, M. A. De Moura

A decimation transformation preceded by a mean-field renormalisation group has been used to obtain the critical properties of various d-dimensional lattices. The method improves substantially both exponents and critical couplings even for small size clusters when compared with decimation and mean-field renormalisation group methods.

Journal of Physics C Solid State Physics•Aug 20, 1984•9 citations

Corner critical exponents from the mean-field renormalisation group

Joseph O. Indekeu, G. Menu

The previously introduced method of mean-field renormalisation has provided a unified approach to bulk and surface critical behaviour. The method is used for the computation of the critical exponent associated with the order parameter at corners. Applications to the square and triangular Ising model are presented. The angle dependence of the corner critical exponent is qualitatively reproduced. The results for the bulk critical exponents are more accurate than in previously employed mean-field renormalisation schemes.

Journal of Physics A Mathematical and General•May 7, 1988•2 citations

MEAN-FIELD RENORMALIZATION GROUP: BIBLIOGRAPHY AND NEW APPLICATIONS USING LARGE CLUSTERS

Kathleen Croes, Joseph O. Indekeu

Renormalization group recursions based on mean-field approximations [J. O. Indekeu, A. Maritan, and A. L. Stella, J. Phys.A15, L291 (1982)], commonly referred to as mean-field renormalization group methods (MFRG), have proven to be efficient and easily applicable for computing non-classical critical properties of lattice models. We give a fairly complete bibliography of applications to date, and extend previous test calculations of bulk, surface, and corner critical exponents in the two-dimensional Ising model to larger cluster sizes on triangular, square (including crossing bonds), and honeycomb lattices. Without much effort the exact value of the critical exponent ratioyH/yT is reproduced systematically with a precision of 2%. This ratio turns out to be the most accurate probe of non-classical critical behaviour that is available in the MFRG method.

Modern Physics Letters B•Apr 30, 1993•16 citations

Mean-field renormalization group: Unified approach to bulk and surface critical behavior

Joseph O. Indekeu, Amos Maritan, Attilio L. Stella

The previously introduced method of mean-field renormalization is reexamined in a finite-size-scaling perspective. The method is shown to provide simultaneously estimates for bulk and surface critical exponents. These are obtained within a scheme which guarantees convergence to exact results assuming the validity of standard finite-size scaling. The unifying scheme leads to rather accurate computations as illustrated in Ising and Potts models in two (and three) dimensions.

Physical review. B, Condensed matter•Jan 1, 1987•66 citations

Mean field-finite size scaling transformations for the Z4spin model

José A. Riera

The recursion relations which result from the scaling law for the magnetisations of two finite systems surrounded by the mean field are obtained for the Z 4 spin model. Then, following a renormalisation group strategy, the phase diagrams and critical exponents are determined and studied. This method leads to a substantial improvement, at least for determining phase diagrams, with respect to mean field approximation or other renormalisation group techniques.

Journal of Physics A Mathematical and General•Oct 1, 1984•1 citation
Various modifications of the mean-field renormalisation group method are analysed to study the convergence of the critical coupling and critical exponents to their exact values as the cluster size increases. Appropriate choice of the length scaling factor or of the scaling quantity can give appreciable improvement over the conventional procedure for short clusters. The best values are achieved when both the bulk and surface critical behaviour are explicitly taken into account.
Two recently proposed methods, the variational cluster wavefunction approximation and the mean-field-like renormalisation group transformation, are used to describe the phase transitions in the Hamiltonian version of the two-dimensional Z(q) symmetric spin models. The convergence of the two schemes to the known results is analysed. It is shown that in their usual form neither of these models can reproduce fine details of the phase diagram, although the renormalisation group method gives in general better convergence.
The previously introduced method of mean-field renormalisation has provided a unified approach to bulk and surface critical behaviour. The method is used for the computation of the critical exponent associated with the order parameter at corners. Applications to the square and triangular Ising model are presented. The angle dependence of the corner critical exponent is qualitatively reproduced. The results for the bulk critical exponents are more accurate than in previously employed mean-field renormalisation schemes.
Renormalization group recursions based on mean-field approximations [J. O. Indekeu, A. Maritan, and A. L. Stella, J. Phys.A15, L291 (1982)], commonly referred to as mean-field renormalization group methods (MFRG), have proven to be efficient and easily applicable for computing non-classical critical properties of lattice models. We give a fairly complete bibliography of applications to date, and extend previous test calculations of bulk, surface, and corner critical exponents in the two-dimensional Ising model to larger cluster sizes on triangular, square (including crossing bonds), and honeycomb lattices. Without much effort the exact value of the critical exponent ratioyH/yT is reproduced systematically with a precision of 2%. This ratio turns out to be the most accurate probe of non-classical critical behaviour that is available in the MFRG method.