  We propose that weak continuous probing may be exploited to determine and
define quantum phases of complex many-body systems based on the measurement
record alone. We test the resulting phase criterion in numerical simulations of
measurements on the Bose-Hubbard model and the quantum Ising chain. This yields
a phase transition point in reasonable agreement with the quantum phase
transition in the ground state of the closed system in the thermodynamic limit,
despite the system being highly excited through the measurement dynamics. At
high measurement strengths, the system's response enters a Zeno regime
suppressing transitions between eigenstates of the measurement operator.
