Phase behavior of a two-dimensional quenched–annealed lattice gas with nearest-neighbor attraction. Grand canonical Monte Carlo simulation

We performed Monte Carlo simulation of the phase diagram of a two-dimensional lattice with the nearest-neighbor attraction on a hexagonal lattice. A fraction of sites is rigidly fixed in a disordered configuration in order to mimic quenched absorbent (matrix). It is shown that the phase diagram of this partly quenched system is essentially narrower and the critical temperature is lower, compared with the bulk system, i.e. without matrix. Moreover, a liquid-like branch of the coexistence envelope has a specific shape. It is shown that different, thermodynamically equivalent, matrix configurations result in a slightly different gas-liquid critical temperature. We have analyzed profoundly thermodynamic behavior of a fluid in each copy of the matrix realization. In particular, the behavior of the heat capacity, of the fourth Binder cumulant, compressibility of a fluid along coexistence are analyzed. The pair distribution function of fluid species and its blocking term, due to correlations of fluid particles via matrix subsystem, have been obtained. The blocking distribution function appears to be more long ranged than the total fluid–fluid distribution function. The fluctuations of the blocking effects may serve as a measure of the number of matrix realizations necessary to involve in obtaining adequate statistical averages in the partly quenched systems.