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 the Physical Society of Japan

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

Hiroki Nakano, Minoru Takahashi

Published Mar 15, 1994• 23 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.63.926

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

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

Hiroki Nakano, Masahiro Takahashi

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.

arXiv:cond-mat/9505066•Physical review. B, Condensed matter•Sep 1, 1995•48 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

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

Thermodynamics of the frustrated ferromagnetic spin-1/2 Heisenberg chain

Johannes Richter, M Härtel, D Ihle +1 more

We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.

arXiv:0811.3549•Journal of Physics Conference Series•Jan 1, 2009•6 citations

Thermodynamic properties of the XXZ ferromagnetic chain with long-range interactions

Lei Shu-guo

The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.

Journal of Anhui University•Jan 1, 2008•0 citations
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 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.
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}}$Si{\mathbf{S}}_{\mathit{i}}Si​\ensuremath{\cdot}Sj{\mathbf{S}}_{\mathit{j}}Sj​ -HJj{\mathcal{J}}_{\mathit{j}}Jj​Sjz{\mathit{S}}_{\mathit{j}}^{\mathit{z}}Sjz​. 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.
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.
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.
We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.
The one-dimensional spin-1/2 Heisenberg XXZ ferromagnetic chain with uniform long-range interactions among the z components of the spins in the transverse field was studied by using the mean-field Jordan-Wigner transformation.The analytic expressions and the numerical results of the thermodynamic quantities,including the Helmholtz free energy,internal energy,specific heat,magnetization and isothermal susceptibility,were obtained.We also discussed the phase transitions of the system at a finite temperature.Our results agreed with that from other literatures in the degenerate condition.