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Communications in Theoretical Physics

Functional Integrals and Free Energy in sine-Gordon–Thirring Model with Impurity Coupling

Jun Yan

Published Oct 1, 2007• 6 citations
Publisher

Abstract

The free energy at low temperature in 1D sine-Gordon–Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon–Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.

DOI
10.1088/0253-6102/48/4/017

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The free energy at low temperature in 1D sine-Gordon–Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon–Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose field method.
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.
This paper determines the zero-temperature equation of state for the massive Thirring / sine-Gordon model. This demonstrates recently derived model-independent upper and lower bounds on the zero-temperature equation of state with fixed number density from systems with a nonzero current density. That approach is potentially valuable as Monte Carlo calculations with a current density avoid the sign problem in the Euclidean formulation. An advantage to illustrating these bounds in the massive Thirring/sine-Gordon model is that the relevant calculations with both a number density and a current density can be done using a Bethe ansatz. For this model, optimal bounds constrain the energy density as a function of number density by a factor of two from above and below at high densities for all choices of couplings. The lower bound becomes exact at low densities, while the upper bound approaches the worst constraint of a factor of 4.90 .