Solution of disordered microphases in the Bethe approximation

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