For a fluid in which the interaction potential has a hard core plus a negative part, softening of the hard core can produce a second transition if a first already exists. We give a general argument for the occurrence of the second transition in the lattice gas, plus explicit results for one-dimensional fluid models with two first-order transitions. One such model also provides an example of the breakdown of the law of rectilinear diameters.

• Received 1 May 1970

DOI:https://doi.org/10.1103/PhysRevLett.24.1284