Surface of dense phase in lattice-gas fluid with long-range interaction

A lattice gas with long-range interaction can simulate phase separation in the system consisting of one kind of component particle like the liquid-vapor theory of van der Waals. The generated phases are distinguished from each other by their particle density. In lattice-gas fluid with long-range interaction, the phase with high density can be observed in the phase with low density like the droplet in vapor. In this paper, the surface of the droplet in lattice-gas fluid with the long-range interaction is determined from the local density and its position is compared with that of Gibbs's dividing surface. The inside region and the outside region of the droplet are defined on the basis of the mean free path in each region. The surface tension is calculated through Laplace's formula using the droplet radius and the pressures in both regions. It is shown that the surface thickness becomes 4r where r is the distance of the long-range interaction.