  We investigate the possibility of a bistable phase in an open many-body
system. To this end we discuss the microscopic dynamics of a continuously
off-resonantly driven Rydberg lattice gas in the regime of strong decoherence.
Our experimental results reveal a prolongation of the temporal correlations
with respect to the lifetime of a single Rydberg excitation and show strong
evidence for the formation of finite-sized Rydberg excitation clusters in the
steady state. We simulate our data using a simplified and a full many-body
rate-equation model. The results are compatible with the formation of
metastable states associated with a bimodal counting distribution as well as
dynamic hysteresis. A scaling analysis reveals however, that the correlation
times remain finite for all relevant system parameters. This suggest that the
Rydberg aggregate is composed of many small clusters and all correlation
lengths remain finite. This is a strong indication for the absence of a global
bistable phase, previously suggested to exist in this system.
