Critical dynamics of long-range models on dynamical Lévy lattices

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