Homogeneous-inhomogeneous transitions in a Landau level with spin splitting

The homogeneous-inhomogeneous transitions of a two-dimensional electron gas in a strong perpendicular magnetic field are studied in the particular case when half of the states in a spin splitted Landau level are occupied. To this end the dielectric susceptibility in the homogeneous states as well as the free energy in the modulated states are calculated. Unless theg factor dos not exceed a certain value the charge-density waves are stable in an interval of finite temperatures.