  Certain higher dimensional operators of the lagrangian may render the vacuum
inhomogeneous. A rather rich phase structure of the phi4 scalar model in four
dimensions is presented by means of the mean-field approximation. One finds
para- ferro- ferri- and antiferromagnetic phases and
commensurate-incommensurate transitions. There are several particles described
by the same quantum field in a manner similar to the species doubling of the
lattice fermions. It is pointed out that chiral bosons can be introduced in the
lattice regularized theory.
