Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
arXiv:math/9911106 · doi:10.1063/1.533180
Abstract
The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results which have been obtained, both in two and higher dimensions. In particular, we describe how the phenomenological Wulff and Winterbottom constructions can be derived from the microscopic description provided by the equilibrium statistical mechanics of lattice gases. We focus on the main conceptual issues and describe the central ideas of the existing approaches.
To appear in the March 2000 special issue of Journal of Mathematical Physics on Probabilistic Methods in Statistical Physics
Cited by in corpus (21)
- On the formation/dissolution of equilibrium droplets
- Fluctuation theory of connectivities for subcritical random cluster models
- Critical region for droplet formation in the two-dimensional Ising model
- Crossing the coexistence line at constant magnetization
- Droplets in the coexistence region of the two-dimensional Ising model
- Moderate deviations for stabilizing functionals in geometric probability
- Large-deviations/thermodynamic approach to percolation on the complete graph
- A proof of the Gibbs-Thomson formula in the droplet formation regime
- Isoperimetry in two-dimensional percolation
- Winterbottom Construction for Finite Range Ferromagnetic Models: An L_1 Approach
- Eigenvalue vs perimeter in a shape theorem for self-interacting random walks
- Surface tension in the dilute Ising model. The Wulff construction
- A coarse graining for the Fortuin-Kasteleyn measure in random media
- Examples of DLR states which are not weak limits of finite volume Gibbs measures with deterministic boundary conditions
- 3D crystal: how flat its flat facets are?
- Colligative properties of solutions: I. Fixed concentrations
- Zero temperature limit for interacting Brownian particles. I. Motion of a single body
- Colligative properties of solutions: II. Vanishing concentrations
- Fixed-magnetization Ising model with a slowly varying magnetic field
- Crystals in the Void
- Phenomenological theory of the Potts model evaporation-condensation transition