Surface tension in the dilute Ising model. The Wulff construction

DOI10.1007/s00220-009-0782-8zbMath1168.82007arXiv0804.2208OpenAlexW1981363655MaRDI QIDQ1028564

Marc Wouts

Publication date: 6 July 2009

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

Full work available at URL: https://arxiv.org/abs/0804.2208

Mathematics Subject Classification ID

Large deviations (60F10) 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

Surface tension and \(\Gamma\)-convergence of Van der Waals-Cahn-Hilliard phase transitions in stationary ergodic media, Metastability in the dilute Ising model, Slow dynamics for the dilute Ising model in the phase coexistence region, Variational problems with percolation: dilute spin systems at zero temperature, Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolation, A coarse graining for the Fortuin-Kasteleyn measure in random media, Asymptotic behaviour of ground states for mixtures of ferromagnetic and antiferromagnetic interactions in a dilute regime

Cites Work

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• A coarse graining for the Fortuin-Kasteleyn measure in random media
• On the small maximal flows in first passage percolation
• Surfaces with minimal random weights and maximal flows: a higher dimensional version of first-passage percolation
• Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
• The shape of the limit set in Richardson's growth model
• Convexity properties of the surface tension and equilibrium crystals
• Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
• Large deviations for the 2D Ising model: A lower bound without cluster expansions
• Graphical representations for Ising systems in external fields
• Bulk transport properties and exponent inequalities for random resistor and flow networks
• On the Wulff crystal in the Ising model.
• Exact large deviation bounds up to \(T_ c\) for the Ising model in two dimensions
• Surface order large deviations for Ising, Potts and percolation models
• Surface order large deviations for high-density percolation
• Slow dynamics for the dilute Ising model in the phase coexistence region
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• The Wulff construction in three and more dimensions
• Shape fluctuations and random matrices
• Critical behavior for maximal flows on the cubic lattice
• Strong disorder for a certain class of directed polymers in a random environment
• The Wulff crystal in Ising and percolation models. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004
• Upper large deviations for the maximal flow in first-passage percolation
• The supercritical phase of percolation is well behaved
• A uniqueness proof for the Wulff Theorem
• Crystalline variational problems
• The Wulff theorem revisited
• Rigorous probabilistic analysis of equilibrium crystal shapes