We study the real-time evolution of large open quantum spin systems in two
spatial dimensions, whose dynamics is entirely driven by a dissipative coupling
to the environment. We consider different dissipative processes and investigate
the real-time evolution from an ordered phase of the Heisenberg or XY-model
towards a disordered phase at late times, disregarding unitary Hamiltonian
dynamics. The corresponding Kossakowski-Lindblad equation is solved via an
efficient cluster algorithm. We find that the symmetry of the dissipative
process determines the time scales which govern the approach towards a new
equilibrium phase at late times. Most notably, we find a slow equilibration if
the dissipative process conserves any of the magnetization Fourier modes. In
these cases, the dynamics can be interpreted as a diffusion process of the
conserved quantity.Comment: 28 pages, 11 figures. Revised version: Presentation reorganized and
one figure adde
