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Journal of Western Chongqing University

Variational Cumulant Expansion Study of Thermodynamical Character of Magnetic Thin Film

Yu Deng

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The variational cumulant expansion method is applied to the thermodyna-mical characters of quantum spin Heisenberg film. The internal energy and specif ic heat are calculated and displayed from the first to the third order. The inte rnal energy is not continueous expect the first order and the specific heat is n ot continueous until the third order in the critical reduced temperature.

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The variational cumulant expansion method is applied to the thermodyna-mical characters of quantum spin Heisenberg film. The internal energy and specif ic heat are calculated and displayed from the first to the third order. The inte rnal energy is not continueous expect the first order and the specific heat is n ot continueous until the third order in the critical reduced temperature.
In order to investigate the variational-cumulant expansion (VCE) method, the 2-dimensional Ising model is expanded to the seventh order by adopting the method of enumerating connected diagrams, in whose process, how to determine the variational parameter is analyzed. The internal energy , specific heat and spontaneous magnetization are calculated from the first order to the seventh order. The results show that the thermodynamic and magnetic quantities converge to the exact values very quickly and the critical point approaches the exact one order by order. The curve-pairing phenomenon is watched between neighboring order curves at high temperature region.
The variational-cumulant-expansion (VCE) method is adopted to calculate the Heisenberg model. The free energy of the model is expanded to the third order, and the analytical formulas for the critical temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ are given for each order. The first order of VCE corresponds to the mean-field theory, the second order gives the same result for Tc{\mathit{T}}_{\mathit{c}}Tc​ as the 1/z expansion, and the third order gives a more complicated correction. As a comparison, the results of the two-dimensional (2D) Ising model for VCE to the seventh order are shown. We carry out a trial to predict the critical temperature of the infinite order of the VCE, and get a very accurate result for the 2D Ising model. A prediction of Tc{\mathit{T}}_{\mathit{c}}Tc​ for the Heisenberg model is also made.