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Phase transitions in one-dimensional classical fluids are usually ruled outby making appeal to van Hove's theorem. A way to circumvent the conclusions ofthe theorem is to consider an interparticle potential that is everywherebounded. Such is the case of, {\it e.g.}, the generalized exponential model ofindex 4 (GEM-4 potential), which in three dimensions gives a reasonabledescription of the effective repulsion between flexible dendrimers in asolution. An extensive Monte Carlo simulation of the one-dimensional GEM-4model [S. Prestipino, {\em Phys. Rev. E} {\bf 90}, 042306 (2014)] has recentlyprovided evidence of an infinite sequence of low-temperature cluster phases,however also suggesting that upon pushing the simulation forward what seemed atrue transition may eventually prove to be only a sharp crossover. We herebyinvestigate this problem theoretically, by three different and increasinglysophisticated approaches ({\it i.e.}, a mean-field theory, the transfer matrixof a lattice model of clusters, and the exact treatment of a system of pointclusters in the continuum), to conclude that the alleged transitions of theone-dimensional GEM4 system are likely just crossovers.

Probing the existence of phase transitions in one-dimensional fluids of penetrable particles