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We use the effective potential method of quantum field theory to obtain thequantum corrections to the zero temperature phase diagram of systems withcompeting order parameters. We are particularly interested in two differentscenarios: regions of the phase diagram where there is a bicritical point, atwhich both phases vanish continuously, and the case where both phases coexisthomogeneously. We consider different types of couplings between the orderparameters, including a bilinear one. This kind of coupling breakstime-reversal symmetry and it is only allowed if both order parameterstransform according to the same irreducible representation. This occurs in manyphysical systems of actual interest like competing spin density waves,different types of orbital antiferromagnetism, elastic instabilities of crystallattices, vortices in a multigap SC and also applies to describe the unusualmagnetism of the heavy fermion compound URu2Si2. Our results show that quantumcorrections have an important effect on the phase diagram of systems withcompeting orders.

Quantum corrections for the phase diagram of systems with competing order