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Markov fields on branching planes

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Publication:1824296
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DOI10.1007/BF01203170zbMath0682.60094MaRDI QIDQ1824296

Chuntao C. Wu, Charles M. Newman

Publication date: 1990

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


zbMATH Keywords

Ising modelsGibbs distributionfree boundary conditiondependent percolation modelsindependent percolation


Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Markov processes (60J99)


Related Items

The Ising model on diluted graphs and strong amenability ⋮ Phase transitions on nonamenable graphs ⋮ Ising models on hyperbolic graphs ⋮ A note on mean-field behavior for self-avoiding walk on branching planes.



Cites Work

  • Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
  • Markov random fields on an infinite tree
  • Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
  • Gibbs States on Countable Sets
  • Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising Models
  • On Ising's model of ferromagnetism
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