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 ( ) 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 =4/5. Here, the system remains homogeneous for small interaction strength ( <4/5), and for anti-ferromagnetic interactions ( <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 =δ/n, where phase separation occurs for δ<−1.