  Lattice models allow for a computationally efficient investigation of
motility-induced phase separation (MIPS) compared to off-lattice systems.
Simulations are less demanding and thus bigger systems can be accessed with
higher accuracy and better statistics. In equilibrium, lattice and off-lattice
models with comparable interactions belong to the same universality class.
Whether concepts of universality also hold for active particles is still a
controversial and open question. Here, we examine two recently proposed active
lattice systems that undergo MIPS and investigate numerically their critical
behaviour. In particular, we examine the claim that these systems and MIPS in
general belong to the Ising universality class. We also take a more detailed
look on the influence and role of rotational diffusion and active velocity in
these systems.
