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Prog. Theor. Phys. Vol. 97 No. 6 (1997) pp. 921-937
The Phase Structure of the Gross-Neveu Model with Thirring Interaction at the Next-to-Leading Order of the 1/N Expansion
Takashi Dateki
Department of Physics, Nagoya University,
Nagoya 464-01
(Received February 4, 1997)
Abstract:
We study the critical behavior of the D(2<D<4)-dimensional Gross-Neveu model with a Thirring interaction,
where a vector-vector type four-fermi interaction is on equal
terms with a scalar-scalar type interaction.
By using an inversion method up to the next-to-leading order of the 1/N
expansion, we construct a gauge invariant effective potential.
We show the existence of the chiral order phase transition,
and determine explicitly the critical surface.
It is observed that the critical behavior is mainly controlled
by the Gross-Neveu coupling g.
The critical surface can be divided into two parts by the surface
g=1, which is the critical coupling in the Gross-Neveu model
at the 1/N next-to-leading order, and the form of the critical surface
is drastically change at g=1.
Comparison with the Schwinger-Dyson (SD) equation is also discussed.
Our result is almost the same as that derived in the SD equation.
In particular, in the case of the pure Gross-Neveu model,
we succeed in deriving exactly the same critical line
as that derived in the SD equation.
URL :
http://ptp.ipap.jp/link?PTP/97/921/
DOI : 10.1143/PTP.97.921
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