  Against common sense, auxetic materials expand or contract perpendicularly
when stretched or compressed, respectively, by uniaxial strain, being
characterized by a negative Poisson's ratio $\nu$. The amount of deformation in
response to the applied force can be at most equal to the imposed one, so that
$\nu=-1$ is the lowest bound for the mechanical stability of solids, a
condition here defined as "hyper-auxeticity". In this work, we numerically show
that ultra-low-crosslinked polymer networks under tension display hyper-auxetic
behavior at a finite crosslinker concentration. At this point, the nearby
mechanical instability triggers the onset of a critical-like transition between
two states of different densities. This phenomenon displays similar features as
well as important differences with respect to gas-liquid phase separation.
Since our model is able to faithfully describe real-world hydrogels, the
present results can be readily tested in laboratory experiments, paving the way
to explore this unconventional phase behavior.
