  Fermion masses can be generated through four-fermion condensates when
symmetries prevent fermion bilinear condensates from forming. This less
explored mechanism of fermion mass generation is responsible for making four
reduced staggered lattice fermions massive at strong couplings in a lattice
model with a local four-fermion coupling. The model has a massless fermion
phase at weak couplings and a massive fermion phase at strong couplings. In
particular there is no spontaneous symmetry breaking of any lattice symmetries
in both these phases. Recently it was discovered that in three space-time
dimensions there is a direct second order phase transition between the two
phases. Here we study the same model in four space-time dimensions and find
results consistent with the existence of a narrow intermediate phase with
fermion bilinear condensates, that separates the two asymptotic phases by
continuous phase transitions.
