  The Gross-Neveu model with chemical potential is investigated as a low-energy
effective theory of polyacetylene. In particular, we focus on the abrupt change
in the features of electric conductivity such as sharp rise in the Pauli
paramagnetism at dopant concentration of about 6%. We will try to explain it by
the finite density phase transition in the Gross-Neveu model. The thermodynamic
Bethe ansatz is combined with the large-N expansion to construct thermodynamics
of the Gross-Neveu model. A first-order phase transition is found in leading
order in the 1/N expansion and it appears to be stable against the 1/N
correction. The next to leading order correction to the critical dopant
concentration is explicitly calculated.
