An order-by-disorder process in the cyclic phase of spin-2 condensate with a weak magnetic field

We present in this paper a model study on the “order-by-disorder” process in the cyclic phase of spin-2 condensate, which forms a family of incommensurable, spiral degenerate ground states. On the basis of the ordering mechanism of entropic splitting, it is demonstrated that the energy corrections resulting from quantum fluctuations of disorder lift the accidental degeneracy of the cyclic configurations and thus lead to an eventual spiral order called the cyclic order. The order-by-disorder phenomenon is then realized even if the magnetic field exists. Finally, we show that our theoretic observations can be verified experimentally by direct detection of the cyclic order in the ⁸⁷Rb condensate of a spin-2 manifold with a weak magnetic field.