Solution of Disordered Microphases in the Bethe approximation
arXiv:2103.14450 · doi:10.1063/5.0052111
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.
arXiv comment15 pages, 5 figures
References in corpus (47)
- The Bethe lattice spin glass revisited
- Phase diagram of patchy colloids: towards empty liquids
- Equilibrium cluster phases and low-density arrested disordered states: The role of short-range attraction and long-range repulsion
- Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion
- Stripe glasses: self generated randomness in a uniformly frustrated system
- Lattice Glass Models
- Phase behavior of a fluid with competing attractive and repulsive interactions
- Colloidal systems with competing interactions: from an arrested repulsive cluster phase to a gel
- Glass models on Bethe lattices
- Equilibrium mechanisms of self-limiting assembly
- Origin of similarity of phase diagrams in amphiphilic and colloidal systems with competing interactions
- Two-dimensional fluid with competing interactions exhibiting microphase separation: theory for bulk and interfacial properties
- Phase transitions in the frustrated Ising model on the square lattice
- Columnar and lamellar phases in attractive colloidal systems
- A model colloidal fluid with competing interactions: bulk and interfacial properties
- Equilibrium Phase Behavior of a Continuous-Space Microphase Former
- Gel to glass transition in simulation of a valence-limited colloidal system
- Magic Numbers for Classical Lennard-Jones Cluster Heat Capacities
- Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers
- Length scale dependent relaxation in colloidal gels
- Self generated randomness, defect wandering and viscous flow in stripe glasses
- Phase diagram of the Ising square lattice with competing interactions
- Structure and Relaxation Dynamics of a Colloidal Gel
- Pattern formation and glassy phase in the theory with screened electrostatic repulsion
- Magnetic Polymer Models for Epigenomic Organisation and Phase Separation
- Nonequilibrium Theory of Epigenomic Microphase Separation in the Cell Nucleus
- Exact solution of the Bose-Hubbard model on the Bethe lattice
- Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
- A Lattice Model for Colloidal Gels and Glasses
- Langevin dynamics of the Coulomb frustrated ferromagnet: a mode-coupling analysis
- Percolation and cluster Monte Carlo dynamics for spin models
- The nature of slow dynamics in a minimal model of frustration-limited domains
- Elastic critical behaviour in a 3d model for polymer gels
- Microphase Equilibrium and Assembly Dynamics
- Evidence for "fragile" glass-forming behavior in the relaxation of Coulomb frustrated three-dimensional systems
- Scaling of Entropic Shear Rigidity
- Self-Assembly of Spiral Patterns in Confined System with Competing Interactions
- Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions
- Clustering and assembly dynamics of a one-dimensional microphase former
- Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model
- A Monte Carlo Approach for Studying Microphases Applied to the Axial Next-Nearest-Neighbor Ising and the Ising-Coulomb Models
- Maximum Valency Lattice Gas Models
- Nonuniversal routes to universality: Critical phenomena in colloidal dispersions
- Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model
- Mean-field phase diagram and spin glass phase of the dipolar Kagome Ising antiferromagnet
- Self-consistent theory for inhomogeneous systems with mesoscopic fluctuations
- Characterization and Efficient Monte Carlo Sampling of Disordered Microphases