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/9505066 · Physical review. B, Condensed matter

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

Hiroki Nakano, Masahiro Takahashi

Published Sep 1, 1995• 48 citations
arXivHTMLPDF

Abstract

Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green's frunction method. The model Hamiltonian is given by scrH=-(${\mathit{J}}_{0}$/2)${\mathcal{J}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{\ensuremath{-}}\mathit{p}}$${\mathbf{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathbf{S}}_{\mathit{j}}$ -H${\mathcal{J}}_{\mathit{j}}$${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$. It is shown that there exists a finite-temperature phase transition in the region dp2d for the d-dimensional case and that no transitions at any finite temperature exist for p\ensuremath{\ge}2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.

DOI
10.1103/physrevb.52.6606

Related papers

Quantum Heisenberg model with long-range ferromagnetic interactions

Hiroki Nakano, Minoru Takahashi

A modified spin-wave theory is applied to the one- and two-dimensional quantum Heisenberg model with long-range ferromagnetic interactions proportional to ${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{p}}$[scrH=-1/2${\mathit{tsum}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$ (${\mathit{J}}_{0}$/${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathit{p}}$)${\mathbf{S}}_{\mathit{i}}$\ensuremath{\cdot}${\mathbf{S}}_{\mathit{j}}$]. It is shown that for dp2d there exists a phase transition at finite temperatures; the critical temperature is estimated. The susceptibility and the specific heat are obtained at low temperatures. Our results for d=1, p=2, and S=1/2 agree with the exact solution of the Haldane-Shastry model. For d=1, we find a scaling relation \ensuremath{\alpha}+1=${\ensuremath{\gamma}}^{\mathrm{\ensuremath{-}}1}$ when 2p3.

arXiv:cond-mat/9311034•Physical review. B, Condensed matter•Oct 1, 1994•54 citations

Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperatures

Hiroki Nakano, Minoru Takahashi

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. ( H =- J ∑ i < j ( r i j ) - p S i · S j ). Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition at a finite temperature for 1< p <2 where the model has longer-range interactions than the HS model. The critical temperature is estimated.

Journal of the Physical Society of Japan•Mar 15, 1994•23 citations

Quantum Heisenberg model with long-range ferromagnetic interactions: A Green’s function approach

Mohamed Hamedoun, Y. Cherriet, Ahmed Hourmatallah +1 more

A Green-function method is employed within a random phase approximation to study the one-dimensional quantum Heisenberg model with long-range ferromagnetic interaction proportional to ${r}^{\ensuremath{-}p}.$ We have shown that for $1<p<2$ there exists a phase transition at finite temperatures and estimate its critical temperature.

Physical review. B, Condensed matter•Mar 28, 2001•23 citations

Classical Heisenberg ferromagnetic chain with long-range interactions: A spectral density approach

A. Cavallo, F. Cosenza, L. De Cesare

The thermodynamic properties of a classical spin-$S$ Heisenberg ferromagnetic chain with long-range interactions in the presence of an external magnetic field are investigated by means of the spectral density method within the framework of the two-time Green's functions in classical statistical mechanics. For exchange interactions decaying as ${r}^{\ensuremath{-}\ensuremath{\alpha}},$ it is shown that long-range order exists at finite temperature for $1<\ensuremath{\alpha}<2$ and that no transition to a ferromagnetic phase at any finite temperature occurs for $\ensuremath{\alpha}>~2,$ consistently with a recent extension of the Mermin-Wagner theorem to spin models with long-range interactions. Besides, by means of a suitable modification of the lowest-order moment equations for the spectral density, the critical temperature and the main critical exponents for $1<\ensuremath{\alpha}<2$ and the low-temperature behavior of the paramagnetic susceptibility for $\ensuremath{\alpha}>~2$ are also obtained. Our results appear in a reasonable agreement with the available exact ones and Monte Carlo calculations.

Physical review. B, Condensed matter•Nov 27, 2002•14 citations

Phase Transition of the Quantum Heisenberg Ferromagnetic Chain with Long-range Interactions

Yonglin Zhao

Within a random phase approximation,the quantum Heisenberg ferromagnetic chain with long-range interaction proportional to r-p was studied by Green-function method.The results indicated that for exchange interaction decaying as r-p for 1p2,there existed a phase transition at finite temperature,and that no transition to a ferromagnetic phase at any finite temperature occurs for p≥2.The results are reasonable agreement with those of the Monte Carlo calculations and the other theoretical approaches.

Journal of Shanxi University•Jan 1, 2007•0 citations

Ferromagnetic Heisenberg chains: A description of the magnetic susceptibility from a noncritical scaling approach

Jean Souletie, Pierre Rabu, Marc Drillon

A noncritical scaling model is reported to describe the behavior of low-dimensional magnetic systems. Unlike the classical phase transition approach, nonsingular solutions are deduced that are worthwhile when correlations exist, but which are not large enough to trigger a long range order at $T\ensuremath{\ne}0$. The notion of ``universality class'' is extended to these systems that stand at or below a lower critical dimensionality, and illustrated for the quantum Heisenberg ferromagnetic chain. In this system, the $T$ dependence of $\ensuremath{\chi}T$ exhibits a power law with a negative critical exponent, $\ensuremath{-}1.25S$, and a negative critical temperature.

Physical Review B•Dec 15, 2005•26 citations
Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green's frunction method. The model Hamiltonian is given by scrH=-(J0{\mathit{J}}_{0}J0​/2){\mathcal{J}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{\ensuremath{-}}\mathit{p}}$${\mathbf{S}}_{\mathit{i}}\ensuremath{\cdot}Sj{\mathbf{S}}_{\mathit{j}}Sj​ -H{\mathcal{J}}_{\mathit{j}}$${\mathit{S}}_{\mathit{j}}^{\mathit{z}}. It is shown that there exists a finite-temperature phase transition in the region dp2d for the d-dimensional case and that no transitions at any finite temperature exist for p\ensuremath{\ge}2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.
A modified spin-wave theory is applied to the one- and two-dimensional quantum Heisenberg model with long-range ferromagnetic interactions proportional to ${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{p}}$[scrH=-1/2${\mathit{tsum}}_{\mathit{i}\mathrm{\ensuremath{\ne}}\mathit{j}}$ (J0{\mathit{J}}_{0}J0​/rijp{\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathit{p}}rijp​)Si{\mathbf{S}}_{\mathit{i}}Si​\ensuremath{\cdot}Sj{\mathbf{S}}_{\mathit{j}}Sj​]. It is shown that for dp2d there exists a phase transition at finite temperatures; the critical temperature is estimated. The susceptibility and the specific heat are obtained at low temperatures. Our results for d=1, p=2, and S=1/2 agree with the exact solution of the Haldane-Shastry model. For d=1, we find a scaling relation \ensuremath{\alpha}+1=${\ensuremath{\gamma}}^{\mathrm{\ensuremath{-}}1}$ when 2p3.
A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. ( H =- J ∑ i < j ( r i j ) - p S i · S j ). Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition at a finite temperature for 1< p <2 where the model has longer-range interactions than the HS model. The critical temperature is estimated.
A Green-function method is employed within a random phase approximation to study the one-dimensional quantum Heisenberg model with long-range ferromagnetic interaction proportional to ${r}^{\ensuremath{-}p}.$ We have shown that for 1<p<21<p<21<p<2 there exists a phase transition at finite temperatures and estimate its critical temperature.
The thermodynamic properties of a classical spin-SSS Heisenberg ferromagnetic chain with long-range interactions in the presence of an external magnetic field are investigated by means of the spectral density method within the framework of the two-time Green's functions in classical statistical mechanics. For exchange interactions decaying as ${r}^{\ensuremath{-}\ensuremath{\alpha}},$ it is shown that long-range order exists at finite temperature for $1<\ensuremath{\alpha}<2$ and that no transition to a ferromagnetic phase at any finite temperature occurs for $\ensuremath{\alpha}>~2,$ consistently with a recent extension of the Mermin-Wagner theorem to spin models with long-range interactions. Besides, by means of a suitable modification of the lowest-order moment equations for the spectral density, the critical temperature and the main critical exponents for $1<\ensuremath{\alpha}<2$ and the low-temperature behavior of the paramagnetic susceptibility for $\ensuremath{\alpha}>~2$ are also obtained. Our results appear in a reasonable agreement with the available exact ones and Monte Carlo calculations.
Within a random phase approximation,the quantum Heisenberg ferromagnetic chain with long-range interaction proportional to r-p was studied by Green-function method.The results indicated that for exchange interaction decaying as r-p for 1p2,there existed a phase transition at finite temperature,and that no transition to a ferromagnetic phase at any finite temperature occurs for p≥2.The results are reasonable agreement with those of the Monte Carlo calculations and the other theoretical approaches.
A noncritical scaling model is reported to describe the behavior of low-dimensional magnetic systems. Unlike the classical phase transition approach, nonsingular solutions are deduced that are worthwhile when correlations exist, but which are not large enough to trigger a long range order at $T\ensuremath{\ne}0$. The notion of ``universality class'' is extended to these systems that stand at or below a lower critical dimensionality, and illustrated for the quantum Heisenberg ferromagnetic chain. In this system, the TTT dependence of $\ensuremath{\chi}T$ exhibits a power law with a negative critical exponent, $\ensuremath{-}1.25S$, and a negative critical temperature.