  We investigate critical equilibrium and out of equilibrium properties of a
ferromagnetic Ising model in one and two dimension in the presence of long
range interactions, $J_{ij}\propto r^{-(d+\sigma)}$. We implement a novel local
dynamics on a dynamical L\'evy lattice, that correctly reproduces the static
critical exponents known in the literature, as a function of the interaction
parameter $\sigma$. Due to its locality the algorithm can be applied to
investigate dynamical properties, of both discrete and continuous long range
models. We consider the relaxation time at the critical temperature and we
measure the dynamical exponent $z$ as a function of the decay parameter
$\sigma$, highlighting that the onset of short range regime for the dynamical
critical properties appears to occur at a value of $\sigma$ which differs from
the equilibrium one.
