  We present an approach to the numerical simulation of open quantum many-body
systems based on the semiclassical framework of the discrete truncated Wigner
approximation. We establish a quantum jump formalism to integrate the quantum
master equation describing the dynamics of the system, which we find to be
exact in both the noninteracting limit and the limit where the system is
described by classical rate equations. We apply our method to simulation of the
paradigmatic dissipative Ising model, where we are able to capture the critical
fluctuations of the system beyond the level of mean-field theory.
