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/0005130 · Journal of Statistical Physics

Linked-Cluster Expansion of the Ising Model

Massimo Campostrini B

Published Apr 1, 2001• 15 citations
arXivHTMLPDF
DOI
10.1023/a:1004884006193

Related papers

Adaptive cluster expansion for Ising spin models

Simona Cocco, Giancarlo Croce, Francesco Zamponi

arXiv:1906.05805•The European Physical Journal B•Nov 1, 2019•2 citations

Cluster expansion and path-integral methods for the transverse Ising model

Zhen‐Ya Li, Qing Jiang

Physics Letters A•Jul 1, 1989•21 citations

New Cluster Method for the Ising Model

Hans Gerd Evertz, H. M. Erkinger, Wolfgang von der Linden

Springer proceedings in physics•Jan 1, 2002•3 citations

Linked-cluster expansion for quantum spin systems and the perpendicular susceptibility of the Ising model

Yung‐Li Wang, Christopher D. Wentworth, B. Westwański

The Wick reduction theorem is used in a linked-cluster-expansion calculation to facilitate the evaluation of the multi-integrals of the ordered products encountered in the expansion. The method resolves a major problem in the general linked-cluster expansion for quantum spin systems. We apply it to the evaluation of the perpendicular susceptibility of the Ising model. An eighth-order linked-cluster series is obtained for a general lattice. The temperature behavior of the perpendicular susceptibility of the three-dimensional Ising model (fcc lattice) is discussed.

Physical review. B, Condensed matter•Aug 1, 1985•30 citations

Equivalence of the linked-cluster expansion and the variational cumulant expansion in the high-temperature limit

Yu Xia, Hao Che, D. L. Lin +1 more

It is shown for the Ising model that the linked-cluster expansion (LCE) is a special case of the variational cumulant expansion (VCE) in the high-temperature limit. The VCE was originally developed and formulated to treat lattice-gauge-field models. The free energy calculated from the VCE with a trial Hamiltonian of mean-field form in the high-temperature limit is in fact identical to that from the LCE. Thus, a more general expansion that is valid for the whole temperature range is established for the treatment of Ising systems.

Physical review. B, Condensed matter•Aug 1, 1992•5 citations

Clusters and Critical Behavior in the Ising Model

Jean-Luc Cambier

•Jan 1, 1985•0 citations
The Wick reduction theorem is used in a linked-cluster-expansion calculation to facilitate the evaluation of the multi-integrals of the ordered products encountered in the expansion. The method resolves a major problem in the general linked-cluster expansion for quantum spin systems. We apply it to the evaluation of the perpendicular susceptibility of the Ising model. An eighth-order linked-cluster series is obtained for a general lattice. The temperature behavior of the perpendicular susceptibility of the three-dimensional Ising model (fcc lattice) is discussed.
It is shown for the Ising model that the linked-cluster expansion (LCE) is a special case of the variational cumulant expansion (VCE) in the high-temperature limit. The VCE was originally developed and formulated to treat lattice-gauge-field models. The free energy calculated from the VCE with a trial Hamiltonian of mean-field form in the high-temperature limit is in fact identical to that from the LCE. Thus, a more general expansion that is valid for the whole temperature range is established for the treatment of Ising systems.