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:cond-mat/0505166

On the low temperature series expansion for the diagonal correlation functions in the two-dimensional Ising model

Ghosh, Ranjan Kumar

Published May 6, 2005• 4 citations
arXivHTMLPDF

Abstract

A previously tested differential equation method for generating low temperature series expansion for diagonal spin-spin correlation functions in the d=2 Ising model is extended to generate the non-universal terms for arbitrary separation of the spins. This extends the earlier calculations of these correlation functions.
DOI
10.48550/arxiv.cond-mat/0505166

Related papers

New method for calculating series expansions of correlation functions in the d=2 Ising model

Ranjan K. Ghosh, Robert E. Shrock

We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the $d=2$ Ising model. The method makes use of a differential equation obeyed by these functions.

Physical review. B, Condensed matter•Jul 1, 1984•6 citations

On general- n coefficients in series expansions for row spin–spin correlation functions in the two-dimensional Ising model

Robert E. Shrock

Abstract We consider spin–spin correlation functions for spins along a row, R n = ⟨ σ 0,0 σ n ,0 ⟩, in the two-dimensional Ising model. We discuss a method for calculating general- n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨ σ 0,0 σ n , n ⟩ in this model.

arXiv:2207.09268•Journal of Physics A Mathematical and Theoretical•Sep 29, 2022•0 citations

Derivation of series expansions for the spin-spin correlation function of the Ising model

Douglas S. Ritchie, J W Essam

A method is described for obtaining perturbation expansions of the pair correlation function about the ferromagnetically ordered state of the S=1/2 Ising model. The expansions take the form of a double power series in temperature and field variables and may be used in any region of the T-H plane of the ferromagnetic and in the disordered region of the antiferromagnet. Coefficients are calculated for the face-centred cubic lattice which allow the low-temperature expansions in zero field to be obtained through u31 and the high-field expansions along the critical isotherm to be obtained through mu 6. Agreement is obtained with existing high-temperature expansions.

Journal of Physics C Solid State Physics•Oct 14, 1977•0 citations

Low-temperature series expansions for the spin-1 Ising model

Ian Graham Enting, Anthony John Guttmann, Iwan Jensen

The finite-lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described which uses two distinct transfer-matrix approaches in order to significantly reduce computer memory requirements and which permits the derivation of the series to 79th order. Subsequent analysis of the series clearly confirms that the spin-1 model has the same dominant critical exponents as the spin- 1/2 Ising model. Accurate estimates for both the critical temperature and non-physical singularities are obtained. In addition, evidence for a non-analytic confluent correction with exponent Delta 1 =1.1+or-0.1 is found.

arXiv:hep-lat/9410005•Journal of Physics A Mathematical and General•Nov 7, 1994•49 citations

Updated tests of scaling and universality for spin-spin correlations in the two- and three- dimensional spin- S Ising models using high-temperature expansions

P. Butera, M. Comi

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-$S$ Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation lengths.

arXiv:hep-lat/0406035•Physical Review B•May 19, 2004•9 citations

Constraints on high-temperature series expansions for spin correlations in the square Ising model

Joseph O. Indekeu

High-temperature series expansions have been derived for pair correlations in the square Ising model with nearest-neighbor and diagonal interactions. Enting has pointed out that constraints on the series expansions can be obtained from exact results on the disorder line of the model. The constraints are imposed on the pair correlation series and turn out to be satisfied by the published series coefficients. The coefficients thus pass a rather severe test. In addition, the constraints allow the prediction of a few extra coefficients.

Physical review. B, Condensed matter•May 1, 1988•1 citation
We exhibit a new method for calculating high-and low-temperature series expansions for diagonal spin-spin correlation functions in the d=2d=2d=2 Ising model. The method makes use of a differential equation obeyed by these functions.
Abstract We consider spin–spin correlation functions for spins along a row, R n = ⟨ σ 0,0 σ n ,0 ⟩, in the two-dimensional Ising model. We discuss a method for calculating general- n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨ σ 0,0 σ n , n ⟩ in this model.
A method is described for obtaining perturbation expansions of the pair correlation function about the ferromagnetically ordered state of the S=1/2 Ising model. The expansions take the form of a double power series in temperature and field variables and may be used in any region of the T-H plane of the ferromagnetic and in the disordered region of the antiferromagnet. Coefficients are calculated for the face-centred cubic lattice which allow the low-temperature expansions in zero field to be obtained through u31 and the high-field expansions along the critical isotherm to be obtained through mu 6. Agreement is obtained with existing high-temperature expansions.
The finite-lattice method of series expansion has been used to extend low-temperature series for the partition function, order parameter and susceptibility of the spin-1 Ising model on the square lattice. A new formalism is described which uses two distinct transfer-matrix approaches in order to significantly reduce computer memory requirements and which permits the derivation of the series to 79th order. Subsequent analysis of the series clearly confirms that the spin-1 model has the same dominant critical exponents as the spin- 1/2 Ising model. Accurate estimates for both the critical temperature and non-physical singularities are obtained. In addition, evidence for a non-analytic confluent correction with exponent Delta 1 =1.1+or-0.1 is found.
We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-SSS Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation lengths.
High-temperature series expansions have been derived for pair correlations in the square Ising model with nearest-neighbor and diagonal interactions. Enting has pointed out that constraints on the series expansions can be obtained from exact results on the disorder line of the model. The constraints are imposed on the pair correlation series and turn out to be satisfied by the published series coefficients. The coefficients thus pass a rather severe test. In addition, the constraints allow the prediction of a few extra coefficients.