Dobrushin-Kotecký-Shlosman theorem for polygonal Markov fields in the plane

DOI10.1007/s10955-006-9053-7zbMath1103.82308arXivmath-ph/0411064OpenAlexW1983621097MaRDI QIDQ2506283

Tomasz Schreiber

Publication date: 28 September 2006

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

Full work available at URL: https://arxiv.org/abs/math-ph/0411064

zbMATH Keywords

phase separationWulff shapeArak-Surgailis polygonal Markov fields.DKS theorem

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

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Cites Work

• Markov fields with polygonal realizations
• Dobrushin-Kotecký-Shlosman theorem up to the critical temperature
• Gaussian limits for random measures in geometric probability
• Loss network representation of Peierls contours
• Consistent polygonal fields
• Perfect simulation for interacting point processes, loss networks and Ising models.
• The thermodynamic limit of polygonal models
• Point-based polygonal models for random graphs
• Rigorous probabilistic analysis of equilibrium crystal shapes
• Spontaneous magnetization in the plane
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