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The extended Hubbard model can host s-wave, d-wave and p-wave superconductingphases depending on the values of the on-site and nearest-neighbourinteractions. Upon detailed examination of the free energy functional of thegap in this model, we show that these symmetries are often dependent ontemperature. The critical points of this functional are constrained by symmetryand allow us to formulate stringent conditions on the temperature profile ofthe gap function, applicable to other models as well. We discuss the finitetemperature phase diagram of the extended Hubbard model, and point out theexistence of symmetry transitions below $T_c$. Understanding the nature ofthese transitions is crucial to assessing the symmetry of unconventionalsuperconductors.

Mixed temperature-dependent order parameters in the extended Hubbard model