The topological Lifshitz phase transition is studied systematically within an
effective model of QCD, in which the chiral symmetry, broken at zero
temperature, is not restored at high temperature and/or baryon chemical
potential. It is found that during phase transition the quark system undergoes
a first-order transition from low density fully-gapped state to high density
state with Fermi sphere which is protected by momentum-space topology. The
Lifshitz phase diagram in the plane of temperature and baryon chemical
potential is established. The critical behaviors of various equations of state
are determined.Comment: 8 pages, 10 figure