  We consider pairwise Markov random fields which have a number of important
applications in statistical physics, image processing and machine learning such
as Ising model and labeling problem to name a couple. Our own motivation comes
from the need to produce synthetic models for social networks with attributes.
First, we give conditions for rapid mixing of the associated Glauber dynamics
and consider interesting particular cases. Then, for pairwise Markov random
fields with submodular energy functions we construct monotone perfect
simulation.
