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The object of the present article is a 1d lattice-gas system comprised ofsoft-particles, wherein particles interact only if they occupy the same or aneighboring site, as a simple representation of penetrable particles of softcondensed matter. To represent different scenarios, two different realizationsof the lattice model are considered, a one-component and a two-componentsystem, where in the two-component case particles of the same species repel andthose of opposite species attract each other. The systems are analyzed entirelywithin the transfer matrix framework. Special attention is paid to thecriterion devised in Ref. [Phys. Rev. E 63, 031206 (2001)], which serves toseparate two classes of behavior encountered in a one-component penetrableparticle systems. In addition to confirm the existence of a similar criterionfor the one-component lattice-gas model, we find that the same criterion can beapplied to the two-component system to provide conditions for thermodynamiccatastrophe.

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