Solution of Disordered Microphases in the Bethe approximation

TL;DR

This paper presents an exact solution for disordered microphases in a SALR model on the Bethe lattice, revealing key structural regimes and insights into their physical properties without homogenization assumptions.

Contribution

It introduces a novel exact Bethe lattice approach to study disordered microphases, capturing their structural complexity beyond mean-field approximations.

Findings

Recapitulates particle and void cluster fluids

Identifies gelation and criticality regimes

Provides insights into glassiness and microphase ordering

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.