  The Gross-Neveu model is a quantum field theory model of Dirac fermions in
two dimensions with a quartic interaction term. Like Yang-Mills theory in four
dimensions, the model is renormalizable (but not super-renormalizable) and
asymptotically free (i.e. its short-distance behaviour is governed by the free
theory). We give a new construction of the massive Euclidean Gross-Neveu model
in infinite volume based on the renormalization group flow equation. The
construction does not involve cluster expansion or discretization of
phase-space. We express the Schwinger functions of the Gross-Neveu model in
terms of the effective potential and construct the effective potential by
solving the flow equation using the Banach fixed point theorem. Since we use
crucially the fact that fermionic fields can be represented as bounded
operators our construction does not extend to models including bosons. However,
it is applicable to other asymptotically free purely fermionic theories such as
the symplectic fermion model.
