  The periodic microphases that self-assemble in systems with competing
short-range attractive and long-range repulsive interactions are structurally
both rich and elegant. Significant theoretical and computational efforts have
thus been dedicated to untangling their properties. By contrast, disordered
microphases, which are structurally just as rich but nowhere near as elegant,
have not been as carefully considered. Part of the difficulty is that simple
mean-field descriptions make a homogeneity assumption that washes away all of
their structural features. Here, we study disordered microphases by exactly
solving a SALR model on the Bethe lattice. By sidestepping the homogenization
assumption, this treatment recapitulates many of the key structural regimes of
disordered microphases, including particle and void cluster fluids as well as
gelation. This analysis also provides physical insight into the relationship
between various structural and thermal observables, between criticality and
physical percolation, as well as between glassiness and microphase ordering.
