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

Journal of Physics C Solid State Physics

Static correlations in one-dimensional easy-axis magnets

Marek Cieplak, A Kryszen

Published Nov 20, 1981• 1 citation
Publisher

Abstract

The static two- and four-spin correlations for one-dimensional easy-axis Heisenberg systems are investigated in the classical limit by means of the transfer matrix method. Both in the high- and low-temperature regions they are found to depend exponentially on the distance between sites. Thus generalisations of the Tomita-Mashiyama recursion relations for the isotropic case can be given. Analytic forms for several types of the correlation functions are obtained for asymptotically low temperatures. These are derived by discussing properties of the second frequency moment of the dynamical structure factor. The dynamical structure factor for the axial components, unlike in the easy-plane systems, should be of non-vanishing width at T=0.

DOI
10.1088/0022-3719/14/32/020

Related papers

Static correlations in one-dimensional classical easy-plane magnets

Marta Z. Cieplak, M. Gutowski, Alf Sjölander

The static two- and four-spin correlations for the one-dimensional easy-plane Heisenberg spin system with a ferromagnetic coupling, like CsNiF 3 , are investigated in the classical limit by means of the transfer matrix method. They are found to consist essentially of two components which both depend exponentially on the distance between sites. Both in the high- and low-temperature regions, only one component remains and this component still dominates at intermediate temperatures. Analytic forms for the correlation functions are given for asymptotically low temperatures. These are obtained by calculating the second-frequency moment of the dynamical structure factor in three different ways, and by requiring the T=0 limit of the moment to coincide with the square of the spin wave frequency. Generalisations of the Tomita-Mashiyama recursion relations (1972) for the isotropic case are given, valid for low temperatures, Monte Carlo calculations of the correlation functions have also been performed and some results of these are presented as well.

Journal of Physics C Solid State Physics•Sep 20, 1980•6 citations

Statistical mechanics of classical one-dimensional Heisenberg ferromagnets with single-site anisotropy

Kazuo Torii Nakamura, Tomohei Sasada

The exact analytical forms of the low-temperature thermodynamic quantities and correlation functions are obtained for classical one-dimensional Heisenberg ferromagnets with single-site anisotropy including both the systems with an easy axis and with an easy plane. The problem has been managed on the basis of the functional integral method. The calculated results have a few leading terms in series-expansion with respect to the reduced temperature, exhibiting the characteristic points borne out in the recent numerical studies. In particular, the longitudinal correlation function and susceptibility of the system with an easy axis show Ising-like behaviours and the transverse counterparts of the system with an easy plane show isotropic XY- or Heisenberg-like behaviours. Physical implications of the calculated results are also discussed.

Journal of Physics C Solid State Physics•Jan 28, 1978•61 citations

Low-temperature thermodynamics and correlation functions for a classical Heisenberg chain with two anisotropies

Hans C. Fogedby, Per Hedegård, A. Svane

The authors derive the thermodynamics and the static correlation functions for the classical Heisenberg chain with the anisotropies within a low-temperature steepest-descent approach. As regards the thermodynamics, they find agreement with transfer matrix and 'ideal-gas' phenomenological results. For the longitudinal correlation function the authors find an antiferromagnetic-type behaviour with a correlation length inversely proportional to the domain wall density. The transverse in-plane correlation function exhibits a damped oscillatory behaviour due to domain-wall-spin interference. The transverse out-of-plane correlations, on the other hand, are exponentially damped with the correlation length increasing as the easy-axis limit is approached.

Journal of Physics C Solid State Physics•Jul 10, 1984•9 citations

Low temperature static behavior of the two-dimensional quantum easy-axis Heisenberg model

S. A. Leonel, Antonio S. T. Pires

We use the self-consistent harmonic approximation (SCHA) to study static properties of the two-dimensional quantum Heisenberg model with easy-axis anisotropy. We calculate the critical temperature as a function of the spin value, and compare with classical results. Specifically, we compare how the ratio of critical temperatures varies as a function of the spin S in the quantum and classical cases, for afixed anisotropy parameter. We see that, for values of spin near 5/2, the classical result approximates to the quantum results and the classical calculation is justified. We have also studied the behavior of the magnetization for very small anisotropies. We have shown that our magnetization curves do not present a plateau in the limit of very small anisotropies, as predicted by the real-space renormalization-group calculations.

Brazilian Journal of Physics•Jun 1, 2000•1 citation

Thermodynamics of two-dimensional XXZ easy-plane quantum Heisenberg magnets

Luca Capriotti, Alessandro Cuccoli, V. Tognetti +2 more

We consider the quantum easy-plane (XXZ) magnet on the square lattice. In the classical case the system exhibits the Berezinskii–Kosterlitz–Thouless transition. Simulations, both for ferro- and antiferromagnets, using the method of the effective classical Hamiltonian, are made for different spin values and refer to the specific heat, the static spin correlation functions and correlation lengths in a broad range of temperatures, below and above the transition. The effects of quantum fluctuations are quantitatively evaluated and discussed.

Journal of Applied Physics•Apr 15, 1997•3 citations

Low-temperature study of magnetic properties of two-dimensional (2d) classical square Heisenberg lattices

Jacques Curély

We start this article by recalling rigorous results previously obtained for 2d square lattices composed of (2N+1)2classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg couplings), in the thermodynamic limit (N→+∞) [4]: (i) the zero-field partition function ZN(0), (ii) the spin correlation which vanishes in the zero-field limit, except at T=0 K so that the critical temperature is TC=0 K, in agreement with Mermin-Wagner's theorem, (iii) the spin-spin correlation between any two lattice sites, (iv) the correlation length and (v) the static susceptibility. We exclusively focus on the low-temperature behaviors of the correlation length and the static susceptibility. This leads to the determination of a diagram characterized by three magnetic phases. Moreover we show that all the behaviors are in perfect agreement with the corresponding ones derived by using a renormalization method. Finally we give criterions allowing to directly determine the magnetic phases characterizing 2d magnetic compounds described by our microscopic model. An experimental test is given for illustrating this theoretical study.

International Conference on Optimization of Electrical and Electronic Equipment•May 1, 2012•1 citation
The static two- and four-spin correlations for one-dimensional easy-axis Heisenberg systems are investigated in the classical limit by means of the transfer matrix method. Both in the high- and low-temperature regions they are found to depend exponentially on the distance between sites. Thus generalisations of the Tomita-Mashiyama recursion relations for the isotropic case can be given. Analytic forms for several types of the correlation functions are obtained for asymptotically low temperatures. These are derived by discussing properties of the second frequency moment of the dynamical structure factor. The dynamical structure factor for the axial components, unlike in the easy-plane systems, should be of non-vanishing width at T=0.
The static two- and four-spin correlations for the one-dimensional easy-plane Heisenberg spin system with a ferromagnetic coupling, like CsNiF 3 , are investigated in the classical limit by means of the transfer matrix method. They are found to consist essentially of two components which both depend exponentially on the distance between sites. Both in the high- and low-temperature regions, only one component remains and this component still dominates at intermediate temperatures. Analytic forms for the correlation functions are given for asymptotically low temperatures. These are obtained by calculating the second-frequency moment of the dynamical structure factor in three different ways, and by requiring the T=0 limit of the moment to coincide with the square of the spin wave frequency. Generalisations of the Tomita-Mashiyama recursion relations (1972) for the isotropic case are given, valid for low temperatures, Monte Carlo calculations of the correlation functions have also been performed and some results of these are presented as well.
The exact analytical forms of the low-temperature thermodynamic quantities and correlation functions are obtained for classical one-dimensional Heisenberg ferromagnets with single-site anisotropy including both the systems with an easy axis and with an easy plane. The problem has been managed on the basis of the functional integral method. The calculated results have a few leading terms in series-expansion with respect to the reduced temperature, exhibiting the characteristic points borne out in the recent numerical studies. In particular, the longitudinal correlation function and susceptibility of the system with an easy axis show Ising-like behaviours and the transverse counterparts of the system with an easy plane show isotropic XY- or Heisenberg-like behaviours. Physical implications of the calculated results are also discussed.
The authors derive the thermodynamics and the static correlation functions for the classical Heisenberg chain with the anisotropies within a low-temperature steepest-descent approach. As regards the thermodynamics, they find agreement with transfer matrix and 'ideal-gas' phenomenological results. For the longitudinal correlation function the authors find an antiferromagnetic-type behaviour with a correlation length inversely proportional to the domain wall density. The transverse in-plane correlation function exhibits a damped oscillatory behaviour due to domain-wall-spin interference. The transverse out-of-plane correlations, on the other hand, are exponentially damped with the correlation length increasing as the easy-axis limit is approached.
We use the self-consistent harmonic approximation (SCHA) to study static properties of the two-dimensional quantum Heisenberg model with easy-axis anisotropy. We calculate the critical temperature as a function of the spin value, and compare with classical results. Specifically, we compare how the ratio of critical temperatures varies as a function of the spin S in the quantum and classical cases, for afixed anisotropy parameter. We see that, for values of spin near 5/2, the classical result approximates to the quantum results and the classical calculation is justified. We have also studied the behavior of the magnetization for very small anisotropies. We have shown that our magnetization curves do not present a plateau in the limit of very small anisotropies, as predicted by the real-space renormalization-group calculations.
We consider the quantum easy-plane (XXZ) magnet on the square lattice. In the classical case the system exhibits the Berezinskii–Kosterlitz–Thouless transition. Simulations, both for ferro- and antiferromagnets, using the method of the effective classical Hamiltonian, are made for different spin values and refer to the specific heat, the static spin correlation functions and correlation lengths in a broad range of temperatures, below and above the transition. The effects of quantum fluctuations are quantitatively evaluated and discussed.
We start this article by recalling rigorous results previously obtained for 2d square lattices composed of (2N+1)2classical spins isotropically coupled between first-nearest neighbors (i.e., showing Heisenberg couplings), in the thermodynamic limit (N→+∞) [4]: (i) the zero-field partition function ZN(0), (ii) the spin correlation which vanishes in the zero-field limit, except at T=0 K so that the critical temperature is TC=0 K, in agreement with Mermin-Wagner's theorem, (iii) the spin-spin correlation between any two lattice sites, (iv) the correlation length and (v) the static susceptibility. We exclusively focus on the low-temperature behaviors of the correlation length and the static susceptibility. This leads to the determination of a diagram characterized by three magnetic phases. Moreover we show that all the behaviors are in perfect agreement with the corresponding ones derived by using a renormalization method. Finally we give criterions allowing to directly determine the magnetic phases characterizing 2d magnetic compounds described by our microscopic model. An experimental test is given for illustrating this theoretical study.