Fates of Exact Finite-$N$ First-Order Transitions: Coherent Suppression versus Spectral-Collapse Termination
Symmetry-protected ground-state crossings can produce exact first-order transitions (FOTs) even at finite $N$, in contrast to continuous transitions governed by soft-mode criticality. We establish exact Juddian ground-state crossings for arbitrary finite $N$ in the one- and two-photon anisotropic Dicke models and ident...