We use a chiral random matrix model with 2Nf flavors to mock up the QCD Dirac spectrum at finite chemical potential. We show that the $1/N$ approximation breaks down in the quenched state with spontaneously broken chiral symmetry. The breakdown condition is set by the divergence of a two-point function that is shown to follow the general lore of macroscopic universality. In this state, the fermionic fluctuations are not suppressed in the large N limit.
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Janik et al. (1996) studied this question.
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