  We numerically study the dynamics and stationary states of a spin ensemble
strongly coupled to a single-mode resonator subjected to loss and external
driving. Employing a generalized cumulant expansion approach we analyze
finite-size corrections to a semiclassical description of amplitude
bistability, which is a paradigm example of a driven-dissipative phase
transition. Our theoretical model allows us to include inhomogeneous broadening
of the spin ensemble and to capture in which way the quantum corrections
approach the semiclassical limit for increasing ensemble size $N$. We set up a
criterion for the validity of the Maxwell-Bloch equations and show that close
to the critical point of amplitude bistability even very large spin ensembles
consisting of up to $10^4$ spins feature significant deviations from the
semiclassical theory.
