Magnetic lattice gas

A spin-1 model of a magnetic lattice gas is presented and analyzed in the limit of infinitely-long-ranged interactions. Phase diagrams are displayed and studied for the whole range of the ratio of magnetic to nonmagnetic interaction strength denoted by $r$. It is shown that there exists a magnetic liquid phase even for a very weak magnetic interaction $r\ll 1$. For a range of medium magnetic interactions, $0.264<r<\mathrm{}0.3604\mathrm{}$, two first-order phase transitions occur; first a nonmagnetic gas to a nonmagnetic liquid phase transition and then a nonmagnetic liquid to a magnetic liquid phase transition occur successively along isotherms at appropriate temperatures.