© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Modern Physics Letters B

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

Kathleen Croes, Joseph O. Indekeu

Published Apr 30, 1993• 16 citations

Abstract

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.

DOI: 10.1142/s0217984993000679

Related papers

Mean field renormalization group for the spin-1/2 XXZ model

Dirk Jan Bukman, J. M. J. van Leeuwen

The mean field renormalization group (MFRG) method is applied to the spin-1/2 XXZ model. The phase diagram is obtained for various lattice structures in two and three dimensions, as well as estimates for the critical exponents. The results of the original MFRG method are quite good, but the more sophisticated approach that also includes surface exponents is not suitable for application to the small clusters used here.

Journal of Physics A Mathematical and General•Aug 21, 1992•3 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

A renormalisation-group method for lattice gas models

A. Šurda

A new method for calculating the critical temperature and critical exponents of classical discrete models, based on the renormalisation-group method and the cluster variational method, is developed. In the lowest approximation, using the mean field approximation and quasichemical approximation, the results for the two-dimensional Ising model are obtained within 2% accuracy.

Journal of Physics A Mathematical and General•Sep 11, 1984•3 citations

Critical properties of the classical Heisenberg and XY models : A mean field renormalization group study

Azam Sadeghi, Farhad Shahbazi

Using both mean field renormalization group (MFRG) and Surface-Bulk MFRG (SBMFRG), we study the critical behavior of the classical Heisenberg and XY models on a simple cubic lattice. Critical temperatures as well as critical exponents, characteristic the universality classes of these two models were calculated, analytically for1, 2, 3 and 4 spin clusters. The results are in good agreement with higher accurate methods such as Monte Carlo and High- temperature series.

Iranian Journal of Physics Research•Jun 15, 2007•0 citations

Anisotropic triangular Ising model in the extended mean-field renormalization-group approach

Christos N. Likos

The recently proposed multi-interaction mean-field renormalization technique [C. N. Likos and A. Maritan, Phys. Rev. E 53, 3303 (1996)] is applied to the Ising model on a triangular lattice with equal couplings in two directions and a different coupling in the third, a model equivalent to a square Ising model with additional second-neighbor interactions along a single diagonal direction. Three different clusters are considered and the possible mappings between them are discussed. The estimates for critical couplings and exponents are in satisfactory agreement with exact results. An explanation of the way in which the finite-size features of the method bring about a systematic overestimation of the critical temperature is also given.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Feb 1, 1997•6 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

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.

The recently proposed multi-interaction mean-field renormalization technique [C. N. Likos and A. Maritan, Phys. Rev. E 53, 3303 (1996)] is applied to the Ising model on a triangular lattice with equal couplings in two directions and a different coupling in the third, a model equivalent to a square Ising model with additional second-neighbor interactions along a single diagonal direction. Three different clusters are considered and the possible mappings between them are discussed. The estimates for critical couplings and exponents are in satisfactory agreement with exact results. An explanation of the way in which the finite-size features of the method bring about a systematic overestimation of the critical temperature is also given.

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.