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We consider the 2PI Cornwall-Jackiw-Tomboulis effective action at finitetemperature for a noncommutative real scalar field theory in 4 dimensions, withnoncommutativity among space and time variables. By means of a Rayleig-Ritzvariation, we study the solutions of a stripe type nonuniform background, whichdepends on space and time, and hence on temperature. The analysis in the firstapproximation shows that such solutions appear in the planar limit, as alreadyknown, but also under normal noncommutativity, in an anisotropic region whichhas not been considered. Further we show that the transition from the uniformordered phase to the non uniform one is first order.

Symmetry breaking in nonuniform noncommutative $\lambda\phi^4$ theory at finite temperature