Acta Physica Sinica

MAGNETIC PROPERTIES OF THE RANDOM MIXTURE OF THE ONE-DIMENSIONAL SYSTEM WITH ANISO-TROPIC HEISENBERG EXCHANGE

Zhen‐Ya Li, YANG CHUAN-ZHANG, 苏州大学物理系

Published Jan 1, 1985• 0 citations

Abstract

In this paper, we extend the method proposed in ref. [1] for the calculation of the partition function of the anisotropic Heisenberg spin system, and calculate the specific heat and magnetic susceptibility for random binary mixture of the one-dimensional system with anisotropic Heisenberg exchange.

DOI: 10.7498/aps.34.801

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Acta Physica Sinica

MAGNETIC PROPERTIES OF THE RANDOM MIXTURE OF THE ONE-DIMENSIONAL SYSTEM WITH ANISO-TROPIC HEISENBERG EXCHANGE

Zhen‐Ya Li, YANG CHUAN-ZHANG, 苏州大学物理系

Published Jan 1, 1985• 0 citations

Publisher

Abstract

DOI: 10.7498/aps.34.801

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Statistical Mechanics of the Finite Heisenberg Model. I

Chikao Kawabata, Masuo Suzuki

The eigen-functions and eigen-values of finite three-dimensional Heisenberg models with anisotropy constant as a parameter (spin=1/2) were obtained exactly with the aid of group theoretical technique and by using a high speed computer. The calculated eigenvalues are identical with those obtained by Serber and Dresselhaus for the isotropic simple cubic 2×2×2 lattice. However, it was found that some terms in their full expressions were to be corrected. The zeros of the partition function of the above 2×2×2 lattice have been investigated as functions of the anisotropy parameter both in the complex temperature plane and in the complex magnetic field plane. Thermodynamic functions such as energy, specific heat, magnetization, and susceptibility have been numerically computed for these finite system.The eigen-functions and eigen-values of finite three-dimensional Heisenberg models with anisotropy constant as a parameter (spin=1/2) were obtained exactly with the aid of group theoretical technique and by using a high speed computer. The calculated eigenvalues are identical with those obtained by Serber and Dresselhaus for the isotropic simple cubic 2×2×2 lattice. However, it was found that some terms in their full expressions were to be corrected. The zeros of the partition function of the above 2×2×2 lattice have been investigated as functions of the anisotropy parameter both in the complex temperature plane and in the complex magnetic field plane. Thermodynamic functions such as energy, specific heat, magnetization, and susceptibility have been numerically computed for these finite system.

Journal of the Physical Society of JapanJan 1, 197014 citations

{J}_{z}=0

are obtained exactly for a finite system and for an infinite system with the aid of annihilation and creation operators, and the free energy

F

of the latter is given by $\ensuremath{-}\frac{F}{\mathrm{NkT}}=(\frac{1}{\ensuremath{\pi}})\ensuremath{\int}{0}^{\ensuremath{\pi}}\mathrm{ln}{2cosh{[{{K}_{x}}^{2}+{{K}_{y}}^{2}+2{K}_{x}{K}_{y}cos2\ensuremath{\omega}\ensuremath{-}2C({K}_{x}+{K}_{y})cos\ensuremath{\omega}+{C}^{2}]}^{\frac{1}{2}}}d\ensuremath{\omega},$ where

{K}_{x}=\frac{{J}_{x}}{2kT}

{K}_{y}=\frac{{J}_{y}}{2kT}

C=\frac{m\mathcal{H}}{\mathrm{kT}}

. The case

{J}_{x}={J}_{y}={J}_{z}=J

is discussed with the aid of a high-temperature expansion and of analysis of small systems. Specific heats and susceptibilities in special cases: (i)

{J}_{x}={J}_{y}=J

{J}_{z}=0

, (ii)

{J}_{x}=J

{J}_{y}={J}_{z}=0

, (

{\mathrm{iii}}_{\mathrm{f}}

)

{J}_{x}={J}_{y}=0

{J}_{z}=J>0

, (

{\mathrm{iii}}_{\mathrm{a}}

)

{J}_{x}={J}_{y}=0

{J}_{z}=J<0

, (

{\mathrm{iv}}_{\mathrm{f}}

)

{J}_{x}={J}_{y}={J}_{z}=J>0

, (

{\mathrm{iv}}_{\mathrm{a}}

)

{J}_{x}={J}_{y}={J}_{z}=J<0

are compared and it is shown that (i), (

{\mathrm{iii}}_{\mathrm{a}}

), and (

{\mathrm{iv}}_{\mathrm{a}}

) have the characteristic features of the observed parallel susceptibility of an antiferromagnetic substance, (ii) those of perpendicular susceptibility, and (

{\mathrm{iii}}_{\mathrm{f}}

) and (

{\mathrm{iv}}_{\mathrm{f}}

) those of paramagnetic susceptibility, even though they have no singularities. The distribution of the zeros of the partition function is also discussed.