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Journal of Sichuan Normal University

Statistical Average Values of Functional Integral and Sine-Gordon-Thirring Model

Zou Bo-Xia

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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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.
A variational approach based on the path-integral formulation of the statistical mechanics is applied to calculate the partition function and the related thermodynamic quantities of one-dimensional kink bearing fields. This is done by determining an effective potential which includes in a complete quantum way the linear modes of the field, while treating variationally the nonlinear excitations. The treatment is applied both to integrable systems, like Sine-Gordon and to non integrable ones, like φ 4 and Double Sine-Gordon. The temperature renormalization can be separately studied both for the vacuum and the one-soliton sector in order to find the low temperature properties in self consistent one-loop approximation. Moreover a low-coupling expansion is given and its range of applicability is found to be much wider than the Wigner expansion. Comparisons with quantum Monte-Carlo results and exact results obtained by Bethe Ansatz are presented.
In this thesis, we review recent progresses on Nonlinear Integral Equation approach to finite size effects in two dimensional integrable quantum field theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions to minimal models perturbed by Φ1,3Φ_{1,3}Φ1,3​. Exact calculations of the dependence of energy levels on the size are presented for vacuum and many excited states.