  We study the influence of short-range quantum correlations and classical
spatial correlations on the phase diagram of the dissipative XYZ model by using
a Gutzwiller Monte carlo method and a cluster Gutzwiller ansatz for the wave
function. Considering lattices of finite size we show the emergence of a
ferromagnetic phase, two paramagnetic phases and the possible existence of a
phase transition which is entirely quantum in nature. The inclusion of
short-range quantum correlations has a drastic effect on the phase diagram but
our results show the inclusion of long-range quantum correlations or the use of
more sophisticated methods are needed to quantitatively match the exact
results. A study of the susceptibility tensor shows that reciprocity is broken,
a feature not observed in closed quantum systems.
