Phase transitions in a conservative game of life

We investigate the dynamics of a conservative version Conway's Game Life, in which pair consisting dead and living cell can switch their states following rules but only by swapping positions, irrespective mutual distance. Our study is based on square-lattice simulations as well mean-field calculation. As density cells increased, we identify discontinuous phase transition between an inactive phase, freezes after finite time, active persists indefinitely thermodynamic limit. Further increasing leads system back to via second transition, continuous square lattice