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HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE

Ảnh hưởng của thăng giáng spin lên các tính chất nhiệt động lực học của chuỗi spin lượng tử với mô hình Heisenberg đẳng hướng

Phạm Hương Thảo

Published Oct 10, 2017• 0 citations
Publisher

Abstract

Dependence of the thermodynamic properties of the quantum spin chain on temperature and external magnetic field is investigated using the functional integral method with short range exchange interaction in isotropic Heisenberg model. The results in mean field approximation (MFA) and spin fluctuation approximation (SFA) are showed and compared with ones of other authors. Besides, the spin fluctuation breaks magnetic order in low dimensional spin systems with the short range exchange interaction in the isotropic Heisenberg model without the external magnetic field.

DOI
10.26459/hueuni-jns.v126i1d.4478

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Dependence of the thermodynamic properties of the quantum spin chain on temperature and external magnetic field is investigated using the functional integral method with short range exchange interaction in isotropic Heisenberg model. The results in mean field approximation (MFA) and spin fluctuation approximation (SFA) are showed and compared with ones of other authors. Besides, the spin fluctuation breaks magnetic order in low dimensional spin systems with the short range exchange interaction in the isotropic Heisenberg model without the external magnetic field.
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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.
The spin-1/2 quantum Heisenberg ferromagnet with anisotropic spin exchange interactions in one dimension is investigated by means of the Green's function method and the spin-wave theory. In this paper we use the Holstein-Primakoff transformation to get the approximately Hamiltonian. We show that the magnetic field and anisotropy can have a rather drastic effect on the correlation functions and susceptibilities in the low-temperature region. Our results show that inverse correlation lengths kx and ky are independent of the temperature in the weak magnetic field. kx is less dependent on the anisotropy than ky. These results are consistent with the theoretical and experimental results.
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Thermodynamic properties of antiferromagnetic spin chain with various AFM nearest-neighbor and FM next-nearest-neighbor exchange interactions are studied using functional integral method in J 1 – J 2 Heisenberg model. Besides, the excitation spectrum of the system is also given. The results show that the system has two distinct excitations with no energy gap from the ground state for any permissible values of J 1 and J 2 without single-ion anisotropy. Changing the exchange parameters influences on the thermodynamic properties and the excitation spectra of the system.
The integrable S=1 isotropic quantum spin chain of N atoms, introduced by Takhtajan (1982) and Bubujian (1983), is studied as a function of magnetisation and hence of magnetic field. The methods used are (i) direct numerical diagonalisation for N<or=12, (ii) numerical solution of the Bethe ansatz equations for N=6, 12, 16, 20, 40, (iii) analytic solution of the Bethe ansatz equations for N to infinity . The authors obtain results for the multiple string structure using the first two of these methods, showing the dominance of two-strings in the ground state and elementary excitations. Based on this they calculate the magnetisation as a function of field in the thermodynamic limit, over the whole spin-flop regime. They observe a tracking soft mode in the finite N results and also an energy gap which tends to zero as N to infinity . Their conclusion is that the system behaves much more like the integrable S= 1 / 2 Heisenberg model than the nonintegrable S=1 Heisenberg model.