Universality classes of phase transitions in the steady state of driven, dissipative spin models with Rydberg blockade

We study arrays of driven dissipative two level systems in one and two dimensional lattices, described by rate equations and blockade conditions. Using Monte Carlo simulations we study the steady-state behaviour of the system. We first confirm the absence of a phase transition to a crystalline order in a one dimensional lattice. In two dimensional lattices on the other hand a phase transition to a crystalline phase occurs. We here investigate the universal properties by numerically determining the critical exponents for lattice models with different Z_n symmetries. The latter can be implemented by choice of lattice geometry and blockade radius.