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Journal of Southwest China Normal University

Analytical Study of Thermodynamical Character of Quantum Heisenberg Film

Yang Xiao

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

The variationalcumulant expansion method is applied to the thermodynamical characters of quantum spin heisenberg film. The internal energy and specific heat are calculated and displayed from the first to the third order. The internal energy is not continueous expect the first order and the specific heat is not continueous until the third order in the critical reduced temperature.

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The variationalcumulant expansion method is applied to the thermodynamical characters of quantum spin heisenberg film. The internal energy and specific heat are calculated and displayed from the first to the third order. The internal energy is not continueous expect the first order and the specific heat is not continueous until the third order in the critical reduced temperature.
With the variational cumulant expansion (VCE) method, the thermodynamic behaviors of antiferromagnetic Heisenberg films in simple cubic lattices are studied analytically. From the analytic properties of the free energy, in principle we are able to calculate analytically the critical temperatures and the thermodynamic functions, to any order cumulant as the functions of the number of L (the hyperlayers in the hyperfilm). Explicit expressions for up to the fourth order are given. A comparison with the existing results for 3-dimensional system is given. The effective range of the interaction is obtained from numerical results.
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.
The variational-cumulant expansion (VCE) method is used to calculate the quantum XY model, for which the trial action does not commute with the action , with arbitrary magnitude of spin on various one-, two- and three-dimensional lattices. The free energy of the model is expanded to the third order and the analytical formulae of critical temperature are given for each order. To testify this method in a wider range, the Heisenberg model on different lattices is also calculated, which has more comparable results. Weighted fitting method of statistical mathematics is adopted to predict of infinite order.