  A semimetal-insulator transition in the Hubbard model on the honeycomb
lattice is studied by using the dynamical mean field theory. Electrons in the
honeycomb lattice resemble the Dirac electron liquid and for weak interactions
the system is semimetal. With increasing the local interaction a
semimetal-insulator transition occurs. We find a nonanalytical structure of the
phase transition which consists of a first-order transition line ending in a
second-order transition point and high-temperature crossover line. A phase
separation of semimetal and insulator occurs at low temperatures. Maxwell
construction is performed to determine the first order transition line. The
phase diagram is also presented.
