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Note the similarity of this behavior to that of some lattice models (cf., for example, the dependence of the critical temperature on band filling shown in Fig. 18 of Ref. 3).
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33646626545
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note
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2order parameters, we would presumably have found two second-order (instead of one first-order) phase transitions, in analogy with the similar results in Ref. 12. Clearly, such more elaborate variational calculation would be a necessary first step for an analysis of the critical behavior at these points.
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note
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v is taken into account. However, the expression in Ref. 23 does not admit a small-frequency expansion of the form (A3) because as is well known (Refs. 8 and 31) it has a branch cut along the real axis that crosses the imaginary axis whenever μ>0. (On the other hand, such an expression is the correct starting point for the derivation of a time-dependent Ginzburg-Landau theory (Ref. 23), which obviously involves an expansion along the real axis.)
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