The critical region of strong-coupling lattice QCD in different large-N limits

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We study the critical behavior at nonzero temperature phase transitions of an effective Hamiltonian derived from lattice QCD in the strong-coupling expansion. Following studies of related quantum spin systems that have a similar Hamiltonian, we show that for large Nc and fixed g²Nc, mean field scaling is not expected, and that the critical region has a finite width at Nc=∞. A different behavior rises for Nf→ ∞ and fixed Nc and g²/Nf, which we study in two spatial dimensions and for Nc=1. We find that the width of the critical region is suppressed by 1/Nfᵖ with p=1/2, and argue that a generalization to Nc>1 and to three dimensions will change this only in detail (e.g. the value of p>0), but not in principle. We conclude by stating under what conditions this suppression is expected, and remark on possible realizations of this phenomenon in lattice gauge theories in the continuum.