  We consider the problem of approximate sampling from the finite volume Gibbs
measure with a general pair interaction. We exhibit a parallel dynamics
(Probabilistic Cellular Automaton) which efficiently implements the sampling.
In this dynamics the product measure that gives the new configuration in each
site contains a term that tends to favour the original value of each spin. This
is the main ingredient that allows to prove that the stationary distribution of
the PCA is close in total variation to the Gibbs measure. The presence of the
parameter that drives the "inertial" term mentioned above gives the possibility
to control the degree of parallelism of the numerical implementation of the
dynamics.
