Abstract
The g-model of the one-dimensional (1-D) Fermi gas including the same site interaction g 4 is investigated in the self-consistent harmonic approximation (SCHA) for the Bosonized Hamiltonian. The asymptotic form of the gap of the spin-density excitation is determined at low temperatures. It is found that the phase transition is of first order and the transition exists if g 1‖ < 0 but does not if g 1‖ > 0. The correlation functions for the order parameters of the charge-density wave (CDW) and singlet-superconductor (SS) are evaluated at low temperatures.
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