  The multi-critical behaviour of an approximately scale and conformal
invariant quantum field theory, which can be regarded as the deformation of the
critical Gross-Neveu model in 3+epsilon dimensions by a nearly marginal parity
violating operator, is studied using a large $N$ expansion. When epsilon is
greater than a number of order 1/N, the deformation is marginally relevant and
it is found to exhibit spontaneous breaking of the approximate scale symmetry
accompanied by the appearance of a light scalar in its spectrum. The scalar
mass is parametrically small, of order epsilon times the fermion mass and it
can be identified with a light dilaton. When the dimension is reduced to 3 the
deformation of the Gross-Neveu model becomes marginally irrelevant, what was a
minimum of the potential becomes a maximum and the theory has a
non-perturbative global instability. There is a metastable perturbative phase
where the scalar does not condense and the fermions are massless separated by
an energy barrier with height of order one (rather than N) from an
energetically favoured phase with a runaway condensate.
