  We present a new phase-field model for binary fluids exhibiting typical
signatures of self-glassiness, such as long-time relaxation, ageing and
long-term dynamical arrest. The present model allows the cost of building an
interface to become locally zero, while preserving global positivity of the
overall surface tension. An important consequence of this property, which we
prove analytically, is the emergence of compact configurations of fluid
density. Owing to their finite-size support, these "compactons" can be
arbitrarily superposed, thereby providing a direct link between the ruggedness
of the free-energy landscape and morphological complexity in configurational
space. The analytical picture is supported by numerical simulations of the
proposed phase-field equation.
