Abstract
The free energy of superconductivity and magnetic order is computed with consideration of exchange and electromagnetic effects. We use the Grassman algebra in order to define the path integral over the fermions. Making use of functional derivatives, we compute the effective action in terms of the magnetic and superconductor order parameters and we find a sinusoidal magnetic order associated to a Lifshitz term with quasi-long-range order. The stability of the coexistence region is similar to the nonlinear \ensuremath{\sigma} model in a lower dimension.
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