arXiv:hep-th/9212124 · Submitted to

Introduction to the Thermodynamics of Spin Chains

Luca Mezincescu, Rafael I. Nepomechie

Published Dec 21, 1992• 28 citations

Abstract

We review how to obtain the thermodynamic Bethe Ansatz (TBA) equations for the antiferromagnetic Heisenberg ring in an external magnetic field. We review how to solve these equations for low temperature and small field, and calculate the specific heat and magnetic susceptibility.

DOI: 10.48550/arxiv.hep-th/9212124

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arXiv:hep-th/9212124 · Submitted to

Introduction to the Thermodynamics of Spin Chains

Luca Mezincescu, Rafael I. Nepomechie

Published Dec 21, 1992• 28 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.hep-th/9212124

Related papers

Low-temperature thermodynamics of A2(2) and su(3)-invariant integrable spin chains

Luca Mezincescu, Rafael I. Nepomechie, Paul K. Townsend +1 more

arXiv:hep-th/9212125Nuclear Physics BOct 1, 199332 citations

Low-temperature features of thermodynamics of an open isotropic Heisenberg chain

Andrei A. Zvyagin, A. V. Makarova

Low Temperature PhysicsSep 1, 20040 citations

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We have extracted the leading low-temperature contributions to the specific heat and the magnetic susceptibility from the thermodynamic Bethe-Ansatz equations of the SU(3) invariant ferromagnetic Heisenberg chain of spin 1. The critical exponents for the specific heat, the susceptibility, and the correlation length are $\ensuremath{\alpha}=\ensuremath{-}\frac{1}{2}$, $\ensuremath{\gamma}=2$, and $\ensuremath{\nu}=1$, respectively. The susceptibility and the correlation length exhibit logarithmic corrections, which are quenched by relatively small magnetic fields. In large fields, the energy required to flip a spin gives rise to an exponential activation.We have extracted the leading low-temperature contributions to the specific heat and the magnetic susceptibility from the thermodynamic Bethe-Ansatz equations of the SU(3) invariant ferromagnetic Heisenberg chain of spin 1. The critical exponents for the specific heat, the susceptibility, and the correlation length are $\ensuremath{\alpha}=\ensuremath{-}\frac{1}{2}$, $\ensuremath{\gamma}=2$, and $\ensuremath{\nu}=1$, respectively. The susceptibility and the correlation length exhibit logarithmic corrections, which are quenched by relatively small magnetic fields. In large fields, the energy required to flip a spin gives rise to an exponential activation.

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Thermodynamic properties of the quantum Heisenberg spin chains with

S=1/2,

1, and

3/2

are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.