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Journal of the Physical Society of Japan

Spin Correlation in the One-Dimensional Heisenberg Antiferromagnet with Competing Interactions (Frontiers in Magnetism)

Isao Harada, Yoshihiro Nishiyama, Yoshio Aoyama

Published Jan 1, 2000• 2 citations
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Thermodynamic properties are studied for the one-dimensional spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions. The internal energy, the specific heat, and the two-spin correlation function are calculated by means of the cluster transfer matrix method based on the Suzuki-Trotter equivalence theorem. Special attention is paid to the asymptotic behavior of the two-spin correlation function in the long-distarace limit. It is found that for a certain range of values of the interaction constants and of the temperature, the two-spin correlation function decays with an incommensurate or a higher-order commensurate oscillation as a function of the distance between two spins. We also find that there exists a quantum analog of the disorder line, on which the two-spin correlation function changes its character.

Journal of the Physical Society of Japan•Aug 15, 1988•16 citations
We study the ground-state and finite-temperature properties of the one-dimensional isotropic spin-1/2 Heisenberg magnet with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions which compete with each other. Extrapolating the exact results for finite-size systems of up to 20 spins, we estimate the ground-state energy and the ground-state two-spin correlation function in the infinite-size limit. Using the cluster transfer matrix method, we also calculate the temperature dependence of the internal energy and the specific heat and that of the inverse correlation length and the wave number, by both of which the asymptotic behavior of the two-spin correlation function in the long-distance limit is characterized. We compare the results of these calculations with those obtained previously for the case where the nearest-neighbor interaction is antiferromagnetic.
Thermodynamic properties are studied for the one-dimensional spin-1/2 Heisenberg antiferromagnet with antiferromagnetic first- and second-neighbor exchange interactions. The internal energy, the specific heat, and the two-spin correlation function are calculated by means of the cluster transfer matrix method based on the Suzuki-Trotter equivalence theorem. Special attention is paid to the asymptotic behavior of the two-spin correlation function in the long-distarace limit. It is found that for a certain range of values of the interaction constants and of the temperature, the two-spin correlation function decays with an incommensurate or a higher-order commensurate oscillation as a function of the distance between two spins. We also find that there exists a quantum analog of the disorder line, on which the two-spin correlation function changes its character.