Phase separation transition in a driven diffusive system with anti-ferromagnetic interaction

One-dimensional non-equilibrium systems with short-range interaction can undergo phase transitions from homogeneous states to phase separated states as interaction (ϵ) among particles is increased. One of the model systems where such a transition has been observed is the extended Katz–Lebowitz–Spohn (KLS) model with ferromagnetically interacting particles at ϵ=4/5. Here, the system remains homogeneous for small interaction strength (ϵ<4/5), and for anti-ferromagnetic interactions (ϵ<0). We show that the phase separation transitions can also occur in anti-ferromagnetic systems if interaction among particles depends explicitly on the size of the block (n) they belong to. We study this transition in detail for a specific case ϵ=δ/n, where phase separation occurs for δ<−1.