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

Critical dynamics of long range models on Dynamical L\'evy Lattices