  Soft matter systems are renowned for being able to display complex emerging
phenomena such as clustering phases. Recently, a surprising quantum phase
transition has been revealed in a one-dimensional (1D) system composed of
bosons interacting via a pairwise soft potential in the continuum. It was shown
that the spatial coordinates undergoing two-particle clustering could be mapped
into quantum spin variables of a 1D transverse Ising model. In this work we
investigate the manifestation of an analogous critical phenomenon in 1D
classical fluids of soft particles in the continuum. In particular, we study
the low-temperature behavior of three different classical models of 1D soft
matter, whose inter-particle interactions allow for clustering. The same string
variables highlight that, at the commensurate density for the two-particle
cluster phase, the peculiar pairing of neighboring soft particles can be
nontrivially mapped onto a 1D discrete classical Ising model. We also observe a
related phenomenon, namely the presence of an anomalous peak in the
low-temperature specific heat, thus indicating the emergence of Schottky
phenomenology in a non-magnetic fluid.
