Journal of Mathematical Physics

Binary Kernel Formulation of a Heisenberg Model of Ferromagnetism

Newton I. Greenberg

Published Mar 1, 1963• 6 citations

Abstract

An ideal Heisenberg model of a ferromagnet for spin 12 is studied by considering the model in terms of a spin-deviation lattice gas. Utilizing the general methods of Yang and Lee, a binary kernel function is obtained in terms of which the thermodynamic properties of the lattice gas can be completely expressed. As an example, Dyson's results are rigorously obtained.

DOI: 10.1063/1.1703967

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Journal of Mathematical Physics

Binary Kernel Formulation of a Heisenberg Model of Ferromagnetism

Newton I. Greenberg

Published Mar 1, 1963• 6 citations

Publisher

Abstract

DOI: 10.1063/1.1703967

Related papers

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The one-dimensional spin-1/2 Ising-Heisenberg ferromagnets are studied by the Green's function method at finite temperatures. The Green's function is decoupled in terms of the correlation functions of 〈 ${\mathit{S}}_{0}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{n}}^{\mathit{z}}$ 〉 and 〈 ${\mathit{S}}_{0}^{+}$ ${\mathit{S}}_{\mathit{n}}^{\mathrm{\ensuremath{-}}}$〉 under the constraint of 〈 ${\mathit{S}}^{\mathit{z}}$ 〉=0, from which a set of self-consistent equations are derived and solved numerically. The thermodynamic properties such as internal energy, specific heat, and zero-field parallel susceptibility are calculated. Our results predict the correct behavior for the correlation functions and thermodynamic quantities in the entire temperature region, in agreement both with the exact numerical results on the finite chain and the experimental data.The one-dimensional spin-1/2 Ising-Heisenberg ferromagnets are studied by the Green's function method at finite temperatures. The Green's function is decoupled in terms of the correlation functions of 〈${\mathit{S}}_{0}^{\mathit{z}}$${\mathit{S}}_{\mathit{n}}^{\mathit{z}}$〉 and 〈${\mathit{S}}_{0}^{+}$${\mathit{S}}_{\mathit{n}}^{\mathrm{\ensuremath{-}}}$〉 under the constraint of 〈${\mathit{S}}^{\mathit{z}}$〉=0, from which a set of self-consistent equations are derived and solved numerically. The thermodynamic properties such as internal energy, specific heat, and zero-field parallel susceptibility are calculated. Our results predict the correct behavior for the correlation functions and thermodynamic quantities in the entire temperature region, in agreement both with the exact numerical results on the finite chain and the experimental data.

Physical review. B, Condensed matterFeb 1, 19957 citations

{\mathit{k}}_{\mathit{B}}

T)] with the constant b=4.5\ifmmode\pm\else\textpm\fi{}0.5, which is lower than the prediction (b=2\ensuremath{\pi}) of a modified spin-wave theory. For the simple-cubic lattice, we find that the critical temperature

{\mathit{k}}_{\mathit{B}}

{\mathit{T}}_{\mathit{c}}

/J=1.68\ifmmode\pm\else\textpm\fi{}0.01, and the ratio of the exponents \ensuremath{\gamma}/\ensuremath{\nu}=2.0\ifmmode\pm\else\textpm\fi{}0.05, which are in good agreement with the estimates of the high-temperature series-expansion method.

{\mathit{S}}_{0}^{\mathit{z}}

{\mathit{S}}_{\mathit{n}}^{\mathit{z}}

〉 and 〈

{\mathit{S}}_{0}^{+}

${\mathit{S}}_{\mathit{n}}^{\mathrm{\ensuremath{-}}}$〉 under the constraint of 〈

{\mathit{S}}^{\mathit{z}}

〉=0, from which a set of self-consistent equations are derived and solved numerically. The thermodynamic properties such as internal energy, specific heat, and zero-field parallel susceptibility are calculated. Our results predict the correct behavior for the correlation functions and thermodynamic quantities in the entire temperature region, in agreement both with the exact numerical results on the finite chain and the experimental data.