Constrained variational problem with applications to the Ising model.

DOI10.1007/BF02179548zbMath1081.82547OpenAlexW1994188643MaRDI QIDQ1593417

Senya B. Shlosman, Roberto H. Schonmann

Publication date: 16 January 2001

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

Full work available at URL: https://doi.org/10.1007/bf02179548

zbMATH Keywords

Ising modellarge deviationsboundary effectsWulff shape

Mathematics Subject Classification ID

Differential games and control (49N70) Large deviations (60F10) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24)

Related Items

Critical prewetting in the 2d Ising model, Confinement of Brownian polymers under geometric area tilts, Complete analyticity for 2D Ising completed, Strict convexity of the free energy of the canonical ensemble under decay of correlations, The shape of the \((2+1)\)D SOS surface above a wall, Surface free energy of a finite system without interfaces at low temperatures, Formation of Facets for an Effective Model of Crystal Growth, Surface order large deviations for 2D FK-percolation and Potts models, An invariance principle to Ferrari-Spohn diffusions, Rigorous probabilistic analysis of equilibrium crystal shapes, Rigorous probabilistic analysis of equilibrium crystal shapes, Local and global geometry of the 2D Ising interface in critical prewetting, Equivalences of the large deviation principle for Gibbs measures and critical balance in the Ising model, On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point, Decay of correlations and uniqueness of the Infinite-Volume Gibbs measure of the Canonical ensemble of 1d-lattice systems, \(N^{3/4}\) law in the cubic lattice, 3D crystal: how flat its flat facets are?, Colligative properties of solutions. I: Fixed concentrations, Colligative properties of solutions. II: Vanishing concentrations, Interaction versus entropic repulsion for low temperature Ising polymers, The Airy₂ process and the 3D Ising model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point
• Large deviations for the 2D Ising model: A lower bound without cluster expansions
• Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region
• The droplet in the tube: A case of phase transition in the canonical ensemble
• 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
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.