  The (discrete) Gross-Neveu model is studied in a lattice realization with an
N-component Majorana Wilson fermion field. It has an internal O(N) symmetry in
addition to the euclidean lattice symmetries. The discrete chiral symmetry for
vanishing mass is expected to emerge in the continuum limit only. The lattice
theory is first recast in terms of two-valued bosonic link variables (dimers).
In this representation, which coincides with the loop representation obtained
earlier by Gattringer with the help of eight-vertex-models, the Boltzmann
weight is essentially positive. While standard local updates are possible in
this form we construct a further exact transformation where we generate dimer
configurations as Peierls contours of an Ising model with a local action
residing on plaquettes. For this model a Swendsen-Wang type cluster algorithm
is constructed. At vanishing coupling it is numerically demonstrated to almost
completely eliminate critical slowing down. Although further tests are
required, an avenue to numerical studies of the Gross-Neveu model with
unprecedented precision seems open.
