  We analyse the $3+1$ D equilibrium chiral magnetic effect (CME). We apply
derivative expansion to the Wigner transform of the two - point Green function.
This technique allows us to express the response of electric current to
external electromagnetic field strength through the momentum space topological
invariant. We consider the wide class of the lattice regularizations of quantum
field theory (that includes, in particular, the regularization with Wilson
fermions) and also certain lattice models of solid state physics (including
those of Dirac semimetals). It appears, that in these models the mentioned
topological invariant vanishes identically at nonzero chiral chemical
potential. That means, that the bulk equilibrium CME is absent in those
systems.
