  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.
