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We discuss the evolution of classical multicritical points under pressure and magnetic field in a model proposed to describe uranium compounds. This model has two 5f bands which hybridize with a single itinerant conduction band. The 5f-electrons interact through Coulomb and exchange terms. Three types of orderings are considered: two conventional Spin Density Waves (SDWs) and a new exotic SDW, i. e., with no magnetic moment formation. This exotic SDW is described by a purely imaginary order parameter. This phase is related to a band mixing given by the spin-flip part of the Hund's rule exchange interaction. Our results show that the simultaneous application of pressure and field changes drastically the scenario with the suppression of some multicritical points and the emergence of other ones. Lastly, we suggest that the presence and evolution of classical multicritical points can be, indeed, a useful tool to unveil novel quantum states of matter.
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