Coulomb frustrated first order phase transition and stripes

We apply the Landau theory of phase transitions to describe the formation of stripes and bubbles in a two dimensional charged system. We show that coupling of the order parameter to the charge density dramatically changes the transition. We discuss the scenario where the order parameter is coupled to the charge density as a local temperature. The Coulomb repulsion leads to an instability, similar to the Lifshitz point. In the vicinity of the critical temperature the striped phase dominates the phase diagram. With decreasing of temperature we observe the first order phase transition to the bubbles phase. Further decrease of the temperature leads to transition to the uniform phase.