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Communications in Theoretical Physics

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

Jun Yan

Published Oct 1, 2008• 4 citations
Publisher

Abstract

The free energy in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.

DOI
10.1088/0253-6102/50/4/20

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The free energy in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals and variational-cumulant expansion methods. Two variational parameters are introduced to evaluate free energy and statistical averages. It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.
In this paper,the statistical physics properties of sine-Gordon-Thirring model with impurity coupling are studied by means of functional integral method,and the effective potential is derived for weak coupling model by using a auxiliary Bose field technique.Free energy of the model is obtained from perturbation expansion of functional determinant.Moreover,the four-order statistical average values of two impurities and condensed term are calculated in weak coupling case.The diagrammatic presentations of the effective potential and statistical average values are also given.
The phase structures of one-dimensional quantum sine-Gordon–Thirring model with N-impurities coupling are studied in this paper. The effective actions at finite temperature are derived by means of the perturbation and non-perturbation functional integrals method. The stability of coexistence phase is analyzed respectively in the weak and strong coupling case. It is shown that the coexistence phase is not stable when fermions have an attractive potential g < 0, and the stable coexistence phase can form when fermions have an exclude potential g > 0.
We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.