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We numerically study the dynamics and stationary states of a spin ensemblestrongly coupled to a single-mode resonator subjected to loss and externaldriving. Employing a generalized cumulant expansion approach we analyzefinite-size corrections to a semiclassical description of amplitudebistability, which is a paradigm example of a driven-dissipative phasetransition. Our theoretical model allows us to include inhomogeneous broadeningof the spin ensemble and to capture in which way the quantum correctionsapproach the semiclassical limit for increasing ensemble size $N$. We set up acriterion for the validity of the Maxwell-Bloch equations and show that closeto the critical point of amplitude bistability even very large spin ensemblesconsisting of up to $10^4$ spins feature significant deviations from thesemiclassical theory.

Critical phenomena and nonlinear dynamics in a spin ensemble strongly coupled to a cavity. II. Semiclassical-to-quantum boundary