  Spontaneous symmetry breaking of the light-front Gross-Neveu model is studied
in the framework of the discretized light-cone quantization. Introducing a
scalar auxiliary field and adding its kinetic term, we obtain a constraint on
the longitudinal zero mode of the scalar field. This zero-mode constraint is
solved by using the $1/N$ expansion. In the leading order, we find a nontrivial
solution which gives the fermion nonzero mass and thus breaks the discrete
symmetry of the model. It is essential for obtaining the nontrivial solution to
treat adequately an infrared divergence which appears in the continuum limit.
We also discuss the constituent picture of the model. The Fock vacuum is
trivial and an eigenstate of the light-cone Hamiltonian. In the large $N$
limit, the Hamiltonian consists of the kinetic term of the fermion with dressed
mass and the interaction term of these fermions.
