Soft-particle lattice-gas in 1d: one- and two-component cases

The object of the present article is a 1d lattice-gas system comprised of soft-particles, wherein particles interact only if they occupy the same or a neighboring site, as a simple representation of penetrable particles of soft condensed matter. To represent different scenarios, two different realizations of the lattice model are considered, a one-component and a two-component system, where in the two-component case particles of the same species repel and those of opposite species attract each other. The systems are analyzed entirely within the transfer matrix framework. Special attention is paid to the criterion devised in Ref. [Phys. Rev. E 63, 031206 (2001)], which serves to separate two classes of behavior encountered in a one-component penetrable particle systems. In addition to confirm the existence of a similar criterion for the one-component lattice-gas model, we find that the same criterion can be applied to the two-component system to provide conditions for thermodynamic catastrophe.