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 (SALR) 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, and between glassiness and microphase ordering.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

“…Our analysis shows that such interactions may profoundly affect the phase stability and lead to the appearance of new ionic liquid states. This is relevant also in the context of general interest to the effects of nonnearest neighbor interactions in statistical mechanics [42][43][44][45][46]. We investigate here how this behavior affects the capacitance and energy storage.…”

Avoiding critical slowdown in models with SALR interactions

“…Straightforward generalizations of SW and Wolff algorithms, however, fail to enhance critical sampling for models with frustrated interactions, such as those used to study spin glasses and systems with competing short-range attractive and long-range repulsive (SALR) interactions [17][18][19][20] . In these models, naive KF-CK clusters gel (or percolate) above the critical temperature 21,22 , thus leaving the critical slowdown unaffected.…”

“…This discrepancy hints at a possible inadequacy of the latter scheme, but further insights are needed to understand why. Bethe Lattice -We therefore consider the ANNNI model on a Bethe lattice, which offers (non-ambiguous) non-zero transition temperatures and is also analytically solvable, albeit through the slightly more involved cavity field method 22,44,45 . The resulting phase diagram and percolation temperatures of the JCS clusters as well the PH clusters are shown in Fig.…”