Cyclic phase in F=2 spinor condensate: Long-range order, kinks, and roughening transition

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We study the effect of thermal fluctuations on homogeneous infinite Bose-Einstein condensate with spin F=2 in the cyclic state, when atoms occupy three hyperfine states with mF=0, ± 2. We use both the approach of small-amplitude oscillations and mapping of our model on the sine-Gordon model. We show that thermal fluctuations lead to the existence of the rough phase in one- and two-dimensional systems, when presence of kinks is favorable. The structure and energy of a single kink are found. We also discuss the effect of thermal fluctuations on spin degrees of freedom in F=1 condensate.