We discuss the low-temperature specific heat of the integrable SU(N)- invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank- $m$ tensor representation, especially for the antiferromagnetic coupling. It is known that the linear specific heat coefficient $\gam$ is a function of a field which breaks the SU(N) invariance of the internal degrees of freedom. We calculate the $\gam$ in a zero field and in a small field. The in-field $\gam$ is less than the zero-field $\gam$ as expected since the entropy is reduced in the ordered system. The zero-field $\gam$ is the same as the one obtained by the prediction of the critical behavior of 1D quantum spin systems via conformal field theory. This extends the previous results for N=2 to an arbitrary N.We discuss the low-temperature specific heat of the integrable SU(N)- invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-$m$ tensor representation, especially for the antiferromagnetic coupling. It is known that the linear specific heat coefficient $\gam$ is a function of a field which breaks the SU(N) invariance of the internal degrees of freedom. We calculate the $\gam$ in a zero field and in a small field. The in-field $\gam$ is less than the zero-field $\gam$ as expected since the entropy is reduced in the ordered system. The zero-field $\gam$ is the same as the one obtained by the prediction of the critical behavior of 1D quantum spin systems via conformal field theory. This extends the previous results for N=2 to an arbitrary N.

arXiv:cond-mat/9312046Dec 11, 19930 citations

Heat transport in low-dimensional Heisenberg antiferromagnets

L.S. Lima, Antonio S. T. Pires

Journal of Magnetism and Magnetic MaterialsFeb 9, 20103 citations

Antiferromagnetic chains coupled by weak ferromagnetic interchain interactions

J. Szṅajd

The linear-perturbation renormalization-group transformation is used to study $s=\frac{1}{2}$ spin chains with antiferromagnetic intrachain interactions $J<0$ coupled by weak ferromagnetic interchain interactions ${J}^{\ensuremath{'}}>0$ in the longitudinal external magnetic field H. The field dependence of the specific heat for several models $(XY,$ anisotropic Heisenberg, and Ising) has been found. The specific heat of the one-dimensional models ${(J}^{\ensuremath{'}}=0)$ exhibits a maximum at ${H=H}_{\mathrm{max}}$ which decreases and shifts to higher fields with increasing temperature, and a minimum which disappears for the temperature higher than some characteristic temperature ${T}_{g}.$ For the antiferromagnetic $\mathrm{XY}$ and Ising models the specific-heat maximum is shifted linearly, whereas for the Heisenberg model the shift cannot be fitted to a single power law. For an arbitrary small ferromagnetic interchain interaction ${(J}^{\ensuremath{'}}>0)$ the specific heat as a function of temperature has a singularity characterizing the antiferromagnetic phase transition. From the flow diagram analysis the dependence of the transition temperature on the interchain interaction and the external field has been found.The linear-perturbation renormalization-group transformation is used to study $s=\frac{1}{2}$ spin chains with antiferromagnetic intrachain interactions $J<0$ coupled by weak ferromagnetic interchain interactions ${J}^{\ensuremath{'}}>0$ in the longitudinal external magnetic field H. The field dependence of the specific heat for several models $(XY,$ anisotropic Heisenberg, and Ising) has been found. The specific heat of the one-dimensional models ${(J}^{\ensuremath{'}}=0)$ exhibits a maximum at ${H=H}_{\mathrm{max}}$ which decreases and shifts to higher fields with increasing temperature, and a minimum which disappears for the temperature higher than some characteristic temperature ${T}_{g}.$ For the antiferromagnetic $\mathrm{XY}$ and Ising models the specific-heat maximum is shifted linearly, whereas for the Heisenberg model the shift cannot be fitted to a single power law. For an arbitrary small ferromagnetic interchain interaction ${(J}^{\ensuremath{'}}>0)$ the specific heat as a function of temperature has a singularity characterizing the antiferromagnetic phase transition. From the flow diagram analysis the dependence of the transition temperature on the interchain interaction and the external field has been found.

Physical review. B, Condensed matterNov 18, 20036 citations

The integrable SU(N) Heisenberg model at finite temperature

Henrik Johannesson

Physics Letters AJun 1, 198635 citations

Overcompensated impurities in antiferromagnetic Heisenberg chains

P. Schlottmann

An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.An impurity of spin S′=1/2 is introduced in the Babujian-Takhtajian Heisenberg model of spin S in one dimension. The impurity is located on the mth link of the chain and interacts with both neighboring sites. The interaction between impurity and Heisenberg chain is of a special type so that the integrability is preserved. The diagonalization of the transfer matrices leads to the Bethe ansatz equations of the model. The thermodynamics of the system is studied. For ferromagnetic coupling in the Heisenberg chain, the impurity is locked into the critical behavior of the lattice, i.e., at low temperatures the specific heat is proportional to T1/2 (ferromagnetic magnons) and the susceptibility diverges as T−2 (with logarithmic corrections). For antiferromagnetic coupling and S =1/2 the impurity is just one more site in the chain. If S ≳1/2 the collective properties of impurity and lattice give rise to critical behavior in complete analogy to the overcompensated n-channel Kondo problem. The zero-temperature entropy is finite in zero-field, but zero if the field is nonzero, giving rise to an essential singularity at T=H=0. As a consequence a two-peak structure arises in the specific heat in a small but finite field.

Journal of Applied PhysicsNov 15, 19910 citations

Zero-temperature dynamics of the linear Heisenberg antiferromagnet in a magnetic field

Gerhard H. Muller, H. Beck, J. C. Bonner

Journal of Magnetism and Magnetic MaterialsJan 1, 19803 citations

We discuss the low-temperature specific heat of the integrable SU(N)- invariant Heisenberg model in one dimension with degrees of freedom in the symmetric rank-

m

tensor representation, especially for the antiferromagnetic coupling. It is known that the linear specific heat coefficient $\gam$ is a function of a field which breaks the SU(N) invariance of the internal degrees of freedom. We calculate the $\gam$ in a zero field and in a small field. The in-field $\gam$ is less than the zero-field $\gam$ as expected since the entropy is reduced in the ordered system. The zero-field $\gam$ is the same as the one obtained by the prediction of the critical behavior of 1D quantum spin systems via conformal field theory. This extends the previous results for N=2 to an arbitrary N.

The linear-perturbation renormalization-group transformation is used to study

s=\frac{1}{2}

spin chains with antiferromagnetic intrachain interactions

J<0

coupled by weak ferromagnetic interchain interactions ${J}^{\ensuremath{'}}>0$ in the longitudinal external magnetic field H. The field dependence of the specific heat for several models

(XY,

anisotropic Heisenberg, and Ising) has been found. The specific heat of the one-dimensional models ${(J}^{\ensuremath{'}}=0)$ exhibits a maximum at

{H=H}_{\mathrm{max}}

which decreases and shifts to higher fields with increasing temperature, and a minimum which disappears for the temperature higher than some characteristic temperature

{T}_{g}.

For the antiferromagnetic

\mathrm{XY}

and Ising models the specific-heat maximum is shifted linearly, whereas for the Heisenberg model the shift cannot be fitted to a single power law. For an arbitrary small ferromagnetic interchain interaction ${(J}^{\ensuremath{'}}>0)$ the specific heat as a function of temperature has a singularity characterizing the antiferromagnetic phase transition. From the flow diagram analysis the dependence of the transition temperature on the interchain interaction and the external field has been found.