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 Condensed Matter

The thermodynamics of the anisotropic spin-SXXZ chain in the high-temperature region

Onofre Rojas, S. M. de Souza, E V Corrêa Silva, M. T. Thomaz

Published Nov 25, 2003• 5 citations
Publisher

Abstract

We report analytical calculations of the Helmholtz free energy of non-integrable anisotropic quantum XXZ chains in the high-temperature regime for several values of the spin S . Single-ion anisotropy and interaction with an external magnetic field are taken into account. The seven lowest-order terms in the high-temperature expansion of Helmholtz free energy are obtained. Our results contribute to the existing literature on high-temperature expansions and numerical studies of those models by discussing the effects of anisotropy upon their high-temperature thermodynamic properties, such as the average energy per site, the specific heat and magnetic susceptibility.

DOI
10.1088/0953-8984/15/49/026

Related papers

High-temperature series expansion of the Helmholtz free energy of the quantum spin- S XYZ chain

Onofre Rojas, S. M. de Souza, E. V. Corrêa Silva +1 more

We consider the $XYZ$ chain model of arbitrary spin $S$ in the high-temperature region, with external magnetic field and single-ion anisotropy term. Our high-temperature expansion of the Helmholtz free energy is analytic in the parameters of the model for $S$, which may range from $1∕2$ to the classical limit of infinite spin $(S\ensuremath{\rightarrow}\ensuremath{\infty})$. Our expansion is carried out up to order ${(J\ensuremath{\beta})}^{5}$. Our results agree with numerical results of the specific heat per site for $S=1∕2$, obtained by the Bethe ansatz, with $h=0$ and $D=0$. Finally, we show that the magnetic susceptibility and magnetization of the quantum model can be well approximated by their classical analog in this region of temperature.

arXiv:cond-mat/0510441•Physical Review B•Nov 22, 2005•6 citations

Analytical results for the high-temperature expansion of the one-dimensional s=1XXZ model

Onofre Rojas, E. V. Corrêa Silva, W. A. Moura-Melo +2 more

Recently Rojas et al. [J. Math. Phys. 43, 1390 (2002)] obtained a closed analytical expression for the coefficients of arbitrary order in the cumulant expansion of a one-dimensional periodic chain model with nearest-neighbor interaction and spatial translation invariance; that approach can be applied equally well to both nonintegrable and exact integrable models. Here, we obtain the exact analytic expressions for the six lowest-order terms of the high-temperature expansion of the Helmholtz free energy per site of the nonintegrable one-dimensional spin-$1$ $\mathrm{XXZ}$ Heisenberg model. Our analytical results for the specific heat and the static magnetic susceptibility are compared, up to order ${\ensuremath{\beta}}^{6}$ for the ferromagnetic and antiferromagnetic phases, with the respective numerical results of a periodic chain with ten sites $(N=10)$ and numerical results in the literature [Bl\"ote, Physica B 79, 427 (1975)]. A very good agreement is obtained for both phases in the high-temperature regime.

Physical review. B, Condensed matter•Mar 31, 2003•4 citations

High-temperature expansion of the tetrahedral spin-1/2 and spin-2 XXZ models

Onofre Rojas, E.V. Corrêa Silva, S. M. de Souza +1 more

We apply the cummulant method to obtain the high-temperature expansion of the Helmholtz free energy of the tetrahedral spin-1/2 and spin-2 XXZ models. The tetrahedral model is written as a composite spin-1 XXZ model, and some of its thermodynamic functions are compared to those of the ordinary spin-1 XXZ model. The composite spin-1 model is then mapped onto a fermion model, and it is shown that the contribution of the string Hamiltonian to thermodynamic functions at high temperatures cannot be neglected. The high-temperature expansion of the Helmholtz free energy of the anisotropic spin-$2$ XXZ chain is obtained up to order ${\ensuremath{\beta}}^{6}.$ Our results fit well the numerical quantum Monte Carlo data calculated by Yamamoto [Phys. Rev. B 53, 3364 (1996)] for the isotropic antiferromagnetic Heisenberg chain. We complement his high-temperature expansions for thermodynamic functions with terms of higher order in $\ensuremath{\beta}.$

Physical Review B•Apr 5, 2004•9 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

Thermodynamics of the one-dimensional s=1 XXZ Heisenberg model: analytical results

Onofre Rojas, E.V. Corrêa Silva, W. A. Moura-Melo +2 more

We apply the results recently derived by Rojas et al. to derive the beta-expansion of the Helmholtz free energy of the spin-1 XXZ Heisenberg model up to 5th order in beta. The analytical expansion obtained is valid for all phases of this model. Our curves of the specific heat fit well Bloete's numerical results in the high temperature regime.

arXiv:cond-mat/0210068•Oct 2, 2002•0 citations

Thermodynamic Properties of the XYZ Chain with Long-range Interactions

Lei Shu-guo

The one-dimensional spin-12 XYZ chain in magnet field and uniform long-range interactions are studied by using the Jordan-Wigner transformation and the Gaussion transformation.The thermodynamic quantities results for Helmholtz free energy,the internal energy,the specific heat and the isothermal susceptibility are obtained.We also discussed first and second-order transition of the system at a finite temperature.Our results agree with numerical results of the XYZ spin chain from the other theory.

Journal of Shanxi University•Jan 1, 2009•0 citations
We report analytical calculations of the Helmholtz free energy of non-integrable anisotropic quantum XXZ chains in the high-temperature regime for several values of the spin S . Single-ion anisotropy and interaction with an external magnetic field are taken into account. The seven lowest-order terms in the high-temperature expansion of Helmholtz free energy are obtained. Our results contribute to the existing literature on high-temperature expansions and numerical studies of those models by discussing the effects of anisotropy upon their high-temperature thermodynamic properties, such as the average energy per site, the specific heat and magnetic susceptibility.
We consider the XYZXYZXYZ chain model of arbitrary spin SSS in the high-temperature region, with external magnetic field and single-ion anisotropy term. Our high-temperature expansion of the Helmholtz free energy is analytic in the parameters of the model for SSS, which may range from 1∕21∕21∕2 to the classical limit of infinite spin $(S\ensuremath{\rightarrow}\ensuremath{\infty})$. Our expansion is carried out up to order ${(J\ensuremath{\beta})}^{5}$. Our results agree with numerical results of the specific heat per site for S=1∕2S=1∕2S=1∕2, obtained by the Bethe ansatz, with h=0h=0h=0 and D=0D=0D=0. Finally, we show that the magnetic susceptibility and magnetization of the quantum model can be well approximated by their classical analog in this region of temperature.
Recently Rojas et al. [J. Math. Phys. 43, 1390 (2002)] obtained a closed analytical expression for the coefficients of arbitrary order in the cumulant expansion of a one-dimensional periodic chain model with nearest-neighbor interaction and spatial translation invariance; that approach can be applied equally well to both nonintegrable and exact integrable models. Here, we obtain the exact analytic expressions for the six lowest-order terms of the high-temperature expansion of the Helmholtz free energy per site of the nonintegrable one-dimensional spin-111 XXZ\mathrm{XXZ}XXZ Heisenberg model. Our analytical results for the specific heat and the static magnetic susceptibility are compared, up to order ${\ensuremath{\beta}}^{6}$ for the ferromagnetic and antiferromagnetic phases, with the respective numerical results of a periodic chain with ten sites (N=10)(N=10)(N=10) and numerical results in the literature [Bl\"ote, Physica B 79, 427 (1975)]. A very good agreement is obtained for both phases in the high-temperature regime.
We apply the cummulant method to obtain the high-temperature expansion of the Helmholtz free energy of the tetrahedral spin-1/2 and spin-2 XXZ models. The tetrahedral model is written as a composite spin-1 XXZ model, and some of its thermodynamic functions are compared to those of the ordinary spin-1 XXZ model. The composite spin-1 model is then mapped onto a fermion model, and it is shown that the contribution of the string Hamiltonian to thermodynamic functions at high temperatures cannot be neglected. The high-temperature expansion of the Helmholtz free energy of the anisotropic spin-222 XXZ chain is obtained up to order ${\ensuremath{\beta}}^{6}.$ Our results fit well the numerical quantum Monte Carlo data calculated by Yamamoto [Phys. Rev. B 53, 3364 (1996)] for the isotropic antiferromagnetic Heisenberg chain. We complement his high-temperature expansions for thermodynamic functions with terms of higher order in $\ensuremath{\beta}.$
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.