  We study a classical Ising model on the honeycomb lattice with local two-body
interactions and present strong evidence that at low temperature it realizes a
higher-rank Coulomb liquid with fracton excitations. We show that the
excitations are (type-I) fractons, appearing at the corners of membranes of
spin flips. Because of the three-fold rotational symmetry of the honeycomb
lattice, these membranes can be locally combined such that no excitations are
created, giving rise to a set of ground states described as a liquid of
membranes. We devise a cluster Monte-Carlo algorithm purposefully designed for
this problem that moves pairs of defects, and use it to study the
finite-temperature behavior of the model. We show evidence for a first order
transition from a high-temperature paramagnet to a low-temperature phase whose
correlations precisely match those predicted for a higher-rank Coulomb phase.
