Rigorous probabilistic analysis of equilibrium crystal shapes

DOI10.1063/1.533180zbMath0969.00035arXivmath/9911106OpenAlexW3099487728MaRDI QIDQ5890304

No author found.

Publication date: 20 September 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911106

zbMATH Keywords

Special issueStatistical physicsEquilibrium statistical physicsNonequilibrium statistical physicsProbabilistic techniques

Mathematics Subject Classification ID

Proceedings, conferences, collections, etc. pertaining to probability theory (60-06) Collections of articles of miscellaneous specific interest (00B15) Proceedings, conferences, collections, etc. pertaining to statistical mechanics (82-06)

Related Items

Spectral gap and cutoff phenomenon for the Gibbs sampler of \(\nabla \varphi\) interfaces with convex potential ⋮ Variational problems with percolation: dilute spin systems at zero temperature ⋮ Formation of Facets for an Effective Model of Crystal Growth ⋮ Translation invariant Gibbs states for the Ising model ⋮ Maximal clusters in non-critical percolation and related models ⋮ Interfaces of ground states in Ising models with periodic coefficients ⋮ Surface tension in the dilute Ising model. The Wulff construction ⋮ Homogenization of ferromagnetic energies on Poisson random sets in the plane ⋮ 3D crystal: how flat its flat facets are? ⋮ Colligative properties of solutions. I: Fixed concentrations ⋮ Colligative properties of solutions. II: Vanishing concentrations

Cites Work

• The standard double soap bubble in \(\mathbb{R}^ 2\) uniquely minimizes perimeter
• Semi-infinite Ising model. II: The wetting and layering transitions.
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• On the microscopic validity of the Wulff construction and of the generalized Young equation
• The probabilistic treatment of phase separations in lattice models composed of more than two types of particles
• Convexity properties of the surface tension and equilibrium crystals
• Correlation inequalities on some partially ordered sets
• Wulff droplets and the metastable relaxation of kinetic Ising models
• Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
• The low-temperature phase of Kac-Ising models
• Large deviations for the 2D Ising model: A lower bound without cluster expansions
• Liquid-vapor phase transitions for systems with finite-range interactions
• Domination by product measures
• Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
• Phase diagram of Ising systems with additional long range forces
• Fluctuations of the phase boundary in the 2D Ising ferromagnet
• Harmonic crystal on the wall: A microscopic approach
• Large deviations and continuum limit in the 2D Ising model
• A nonlocal anisotropic model for phase transitions
• Equilibrium shapes of crystals attached to walls.
• Surface tension in Ising systems with Kac potentials.
• Constrained variational problem with applications to the Ising model.
• Constrained minima of nonlocal free energy functionals.
• Large deviations in the van der Waals limit
• Interface, surface tension and reentrant pinning transition in the \(2\)D Ising model
• Pseudo free energies and large deviations for non Gibbsian FKG measures
• Complete analyticity for 2D Ising completed
• Exact large deviation bounds up to \(T_ c\) for the Ising model in two dimensions
• Exponential decay of connectivities in the two-dimensional Ising model
• Surface order large deviations for Ising, Potts and percolation models
• Surface order large deviations for high-density percolation
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• The construction of the \(d+1\)-dimensional Gaussian droplet
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• The Wulff construction in three and more dimensions
• OPEN PROBLEMS IN SOAP BUBBLE GEOMETRY
• A uniqueness proof for the Wulff Theorem
• Crystalline variational problems
• Stability of the interface in a model of phase separation
• On the van der Waals Theory of the Vapor-Liquid Equilibrium. I. Discussion of a One-Dimensional Model
• Rigorous Treatment of the Van Der Waals-Maxwell Theory of the Liquid-Vapor Transition
• The Wulff theorem revisited

This page was built for publication: Rigorous probabilistic analysis of equilibrium crystal shapes