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

International Journal of Theoretical Physics

Anisotropic Heisenberg Magnet with Long-Range Interactions. Integrability and Phase Structure

Vahid Karimipour, Mohammad Khorrami

Published Mar 1, 1999• 0 citations
Publisher
DOI
10.1023/a:1026681624348

Related papers

The anisotropic Heisenberg model in the long-range interaction limit

Paul A. Pearce, Colin J. Thompson

Communications in Mathematical Physics•Jun 1, 1975•50 citations

An exact solution to the classical, anisotropic Heisenberg model with long-range Kac interactions

Kenneth Millard, Harvey S. Leff

Journal of Statistical Physics•Mar 1, 1974•2 citations

Quantum Heisenberg Ferromagnets with Long-Range Interactions

Hiroki Nakano, Minoru Takahashi

Journal of the Physical Society of Japan•Nov 15, 1994•11 citations

Phase transition in two-dimensional magnetic systems with dipolar interactions

L. A. S. Mόl, B. V. Costa

In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.

arXiv:1109.1840•Sep 8, 2011•1 citation

Nonequivalence of ensembles in the Curie–Weiss anisotropic quantum Heisenberg model

Michael Kästner

The microcanonical entropy s ( e , m ) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie–Weiss-type interactions. The result shows a number of interesting properties which are peculiar to long-range interacting systems, including nonequivalence of ensembles and partial equivalence. Furthermore, from the shape of the entropy it follows that the Curie–Weiss Heisenberg model is indistinguishable from the Curie–Weiss Ising model in canonical thermodynamics, although they do in general differ in microcanonical thermodynamics. The possibility of experimentally realizing quantum spin models with long-range interactions in a microcanonical setting by means of cold dipolar gases in optical lattices is discussed.

arXiv:1005.5050•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2010•33 citations

A Exact Solution of the Anisotropic Heisenberg Model with Long Range 'kac' Interactions.

Kenneth Millard

•Jan 1, 1971•1 citation
In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.
The microcanonical entropy s ( e , m ) as a function of the energy e and the magnetization m is computed analytically for the anisotropic quantum Heisenberg model with Curie–Weiss-type interactions. The result shows a number of interesting properties which are peculiar to long-range interacting systems, including nonequivalence of ensembles and partial equivalence. Furthermore, from the shape of the entropy it follows that the Curie–Weiss Heisenberg model is indistinguishable from the Curie–Weiss Ising model in canonical thermodynamics, although they do in general differ in microcanonical thermodynamics. The possibility of experimentally realizing quantum spin models with long-range interactions in a microcanonical setting by means of cold dipolar gases in optical lattices is discussed.