A novel scheme to perform finite‐temperature grand‐canonical simulations of ideal fermions in arbitrary external potentials is introduced. This scheme is based on the evaluation of the grand‐canonical function of lattice fermions. As an application, we present results on the phase behavior of a mixture of fermions and hard spheres. A simple analytic model of solvated fermions in a hard‐sphere fluid is also studied. We address here the possibility of phase separation between a pure delocalized phase of fermions and a homogeneous solution of solvated fermions. These calculations indicate that the homogeneous phase is expected to be stable only at low fermion concentration and low thermal wavelengths. The fermion simulations indicate that such phase separation is a likely scenario.

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