Phase coexistence of gradient Gibbs states

DOI10.1007/s00440-006-0013-6zbMath1120.82003arXivmath/0512502OpenAlexW2129861981MaRDI QIDQ2641898

Marek Biskup, Roman Kotecký

Publication date: 17 August 2007

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512502

zbMATH Keywords

reflection positivitygradient Gibbs measuresenergy entropy transition

Mathematics Subject Classification ID

Random fields (60G60) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (29)

Convergence of deterministic growth models ⋮ Mirror symmetry of height-periodic gradient Gibbs measures of an SOS model on Cayley trees ⋮ Quantitative hydrodynamic limits of the Langevin dynamics for gradient interface models ⋮ Phase transitions for a class of gradient fields ⋮ Continuous spin models on annealed generalized random graphs ⋮ Convergence to the thermodynamic limit for random-field random surfaces ⋮ Scaling limit for a class of gradient fields with nonconvex potentials ⋮ Harmonic deformation of Delaunay triangulations ⋮ Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees ⋮ The maximum of log‐correlated Gaussian fields in random environment ⋮ Recent progress on the random conductance model ⋮ Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees ⋮ Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \(\nabla\phi\) systems with non-convex potential ⋮ Existence of random gradient states ⋮ Nonlinear elastic free energies and gradient Young-Gibbs measures ⋮ Extremal decomposition for random Gibbs measures: from general metastates to metastates on extremal random Gibbs measures ⋮ Extrema of the Two-Dimensional Discrete Gaussian Free Field ⋮ Fixed points of an infinite dimensional operator related to Gibbs measures ⋮ Hydrodynamic limit for the Ginzburg-Landau \(\nabla \phi\) interface model with non-convex potential ⋮ Uniqueness of gradient Gibbs measures with disorder ⋮ Delocalization of two-dimensional random surfaces with hard-core constraints ⋮ Continuous interfaces with disorder: Even strong pinning is too weak in two dimensions ⋮ Nonexistence of random gradient Gibbs measures in continuous interface models in \(d=2\) ⋮ Quantitative hydrodynamic limits of the Langevin dynamics for gradient interface models ⋮ Gradient Gibbs measures for the SOS model with countable values on a Cayley tree ⋮ Strict convexity of the free energy for a class of non-convex gradient models ⋮ Return probability and recurrence for the random walk driven by two-dimensional Gaussian free field ⋮ Models of gradient type with sub-quadratic actions ⋮ Gradient Gibbs measures of an SOS model on Cayley trees: 4-periodic boundary laws

Cites Work

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