  We formulate a model of N_f=4 flavors of relativistic fermion in 2+1d in the
presence of a chemical potential mu coupled to two flavor doublets with
opposite sign, akin to isopsin chemical potential in QCD. This is argued to be
an effective theory for low energy electronic excitations in bilayer graphene,
in which an applied voltage between the layers ensures equal populations of
particles on one layer and holes on the other. The model is then reformulated
on a spacetime lattice using staggered fermions, and in the absence of a sign
problem, simulated using an orthodox hybrid Monte Carlo algorithm. With the
coupling strength chosen to be close to a quantum critical point believed to
exist for N_f<N_fc\approx4.8, it is found that there is a region below
saturation where both the carrier density and a particle-hole "excitonic"
condensate scale anomalously with increasing mu, much more rapidly that the
corresponding quantities in free field theory, while the conventional chiral
condensate is strongly suppressed. The corresponding ground state is speculated
to be a strongly-correlated degenerate fermion system, with a remnant Fermi
surface distorted by a superfluid excitonic condensate. The model thus shows
qualitatively different behaviour to any model with mu=/=0 previously studied
by lattice simulation.
