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We consider a classical lattice gas that consists of more than one ''species'' of particles (like a spin-32 Ising model or the atomic limit of the extended Hubbard model), whose ground-state phase diagram is macroscopically degenerate. This gas is coupled component-wise and in the Falicov-Kimball-like manner to a multicomponent free-fermion gas. We show rigorously that a component-wise coupling of...
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