Exact calculation of the phase properties of one dimensional finite lattice gas systems

The small-size partially filled one-dimensional (1D) lattice gas system with $1/r^\delta $ repulsive interactions is numerically studied. Our results indicate that phase change with vacancy ordering involved exists in the partially filled 1D lattice gas systems, and the phase properties of the studied system strongly depend on the occupancy nav and the interaction strength $\delta $. Most interestingly, it is found that the phase change still exists in the 1D finite-size lattice gas systems even with nearest neighbor interactions, i.e. $\delta $ is infinite. These results provide valuable information about the phase properties of 1D confined systems, such as molecules inside the carbon nanotubes, with long-range interactions between particles