Multi-fermion interaction models in curved spacetime

A model with a scalar type eight-fermion interaction is investigated in curved spacetime. The ground state of the model can be obtained by observing the effective potential. Applying the Riemann normal coordinate expansion, we calculate an effective potential of the model in a weakly curved spacetime. The result is extended to models with multi-fermion interactions. We numerically show the behavior of the effective potential and find the phase structure of the model.