Ring-exchange (RE) interaction in Mott insulator with doubly degenerate $e_g$orbitals is studied. Hamiltonian for the RE interaction is derived by theperturbational calculation. A remarkably weak RE interaction destroys theorbital order caused by the order-by-fluctuation mechanism in thenearest-neighbor exchange-interaction model. A long range order of magneticoctupole moment, i.e. complex orbital wave functions, appears. Competitionbetween octupole and quadrupole interactions strongly suppresses orderedmoments.
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