  We compute the QCD equation of state for zero temperature and finite isospin
density within the Nambu-Jona-Lasinio model in the mean field approximation,
motivated by the recently obtained Lattice QCD results for a new class of
compact stars: pion stars. We have considered both the commonly used
Traditional cutoff Regularization Scheme and the Medium Separation Scheme,
where in the latter purely vacuum contributions are separated in such a way
that one is left with ultraviolet divergent momentum integrals depending only
on vacuum quantities. We have also compared our results with the recent results
from Lattice QCD and Chiral Perturbation Theory.
