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

arXiv:1408.6862 · Journal of Magnetism and Magnetic Materials

Effective field theory in larger clusters – Ising model

Ümit Akıncı

Published Mar 19, 2015• 17 citations
arXivHTMLPDF
DOI
10.1016/j.jmmm.2015.03.063

Related papers

Fluctuating local field method for the disordered Ising model

Daria Kuznetsova, Grigory V. Astretsov, Alexey N. Rubtsov

We present a method for computing thermal properties of classical spin clusters with arbitrarily chosen interactions between spins. For such systems, instability channels are \textit{a priori} not known. The method is based on the Fluctuating Local Field (FLF) approach, the effective description of the system with a nonlinear and fluctuating field, and achieves substantial improvements over mean-field theory. We show that two fluctuating modes are sufficient for numerically accurate solution of systems consisting of two dozen spins, while for larger systems it is needed to account for a larger number of fluctuating modes for a full quantitative agreement with the exact solution.

arXiv:2212.14733•Dec 30, 2022•0 citations

Correlated effective field approximation for the Ising model

G. Bruce Taggart

Physica A Statistical Mechanics and its Applications•Jul 1, 1982•8 citations

Field theory of Ising percolating clusters

Gesualdo Delfino A

arXiv:0902.3339•Nuclear Physics B•Apr 7, 2009•21 citations

Correlated cluster mean-field theory for spin systems

Daisuke Yamamoto

A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a cluster is preserved. Since the strength of interactions of a cluster with its surrounding clusters is strongly dependent on the spin configuration of the central cluster itself, we include this contribution in the effective fields acting on the spins. The effects of ``correlations'' between clusters can be taken into account beyond the standard mean-field level and as a result our cluster-based method gives qualitatively (and even quantitatively) correct results for the both Ising and Heisenberg models. Especially, for the Ising model on the honeycomb and square lattices, the calculated results of the critical temperature are very close (overestimated by only less than 5%) to the exact values.

arXiv:0812.4139•Physical Review B•Apr 24, 2009•69 citations

Effective-field theory on the kinetic spin-3/2 Ising model

Xiaoling Shi, Yang Qi

Journal of Magnetism and Magnetic Materials•Jun 3, 2015•10 citations

Accurate results for Ising models from large order cluster variation method

Alessandro Pelizzola

The cluster variation method is a powerful hierarchy of mean-field-like approximations for Ising-like lattice models, which is known to give results that are particularly accurate at high and/or low temperature and converge to the exact ones as the size of the clusters taken into account gets larger. Here we show how these properties can be exploited to obtain non-classical, quite accurate estimates of quantities characterizing the critical behavior of the ordinary Ising model and the ground state of the triangular Ising antiferromagnet.

AIP conference proceedings•Jan 1, 2001•0 citations
We present a method for computing thermal properties of classical spin clusters with arbitrarily chosen interactions between spins. For such systems, instability channels are \textit{a priori} not known. The method is based on the Fluctuating Local Field (FLF) approach, the effective description of the system with a nonlinear and fluctuating field, and achieves substantial improvements over mean-field theory. We show that two fluctuating modes are sufficient for numerically accurate solution of systems consisting of two dozen spins, while for larger systems it is needed to account for a larger number of fluctuating modes for a full quantitative agreement with the exact solution.
A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a cluster is preserved. Since the strength of interactions of a cluster with its surrounding clusters is strongly dependent on the spin configuration of the central cluster itself, we include this contribution in the effective fields acting on the spins. The effects of ``correlations'' between clusters can be taken into account beyond the standard mean-field level and as a result our cluster-based method gives qualitatively (and even quantitatively) correct results for the both Ising and Heisenberg models. Especially, for the Ising model on the honeycomb and square lattices, the calculated results of the critical temperature are very close (overestimated by only less than 5%) to the exact values.
The cluster variation method is a powerful hierarchy of mean-field-like approximations for Ising-like lattice models, which is known to give results that are particularly accurate at high and/or low temperature and converge to the exact ones as the size of the clusters taken into account gets larger. Here we show how these properties can be exploited to obtain non-classical, quite accurate estimates of quantities characterizing the critical behavior of the ordinary Ising model and the ground state of the triangular Ising antiferromagnet.