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Soft matter systems are renowned for being able to display complex emergingphenomena such as clustering phases. Recently, a surprising quantum phasetransition has been revealed in a one-dimensional (1D) system composed ofbosons interacting via a pairwise soft potential in the continuum. It was shownthat the spatial coordinates undergoing two-particle clustering could be mappedinto quantum spin variables of a 1D transverse Ising model. In this work weinvestigate the manifestation of an analogous critical phenomenon in 1Dclassical fluids of soft particles in the continuum. In particular, we studythe low-temperature behavior of three different classical models of 1D softmatter, whose inter-particle interactions allow for clustering. The same stringvariables highlight that, at the commensurate density for the two-particlecluster phase, the peculiar pairing of neighboring soft particles can benontrivially mapped onto a 1D discrete classical Ising model. We also observe arelated phenomenon, namely the presence of an anomalous peak in thelow-temperature specific heat, thus indicating the emergence of Schottkyphenomenology in a non-magnetic fluid.

Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables