Solution of Disordered Microphases in the Bethe approximation

Abstract

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.

Numerical transfer matrix study of frustrated next-nearest-neighbor Ising models on square lattices

“…(Reference 18 concluded that a continuous transition takes place for κ = 0.48, based on the absence of discontinuity in u(T ), but did not consider the weakly first-order transition scenario.) Interestingly, a recent computation for a low-connectivity Bethe lattice suggests that such a weakly first-order transition in the vicinity of the multicritical point (κ < ∼ 1/2 in the DNNI model) is a mean-field feature [48]. This behavior thus clearly differs from the fluctuation-induced discontinuity of the weakly first-order transition for 1/2 < κ < κ * .…”