Comparison and disjoint-occurrence inequalities for random-cluster models.

DOI10.1007/BF02180133zbMath1080.82546OpenAlexW1963520073MaRDI QIDQ1593203

Geoffrey R. Grimmett

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/bf02180133

zbMATH Keywords

Ising modelPotts modelFKG inequalityBK inequalityrandom-cluster modelcomparison inequality

Mathematics Subject Classification ID

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

Related Items

Explicit isoperimetric constants and phase transitions in the random-cluster model, Mixed percolation as a bridge between site and bond percolation., Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd, A note on exponential decay in the random field Ising model, Random-cluster measures and uniform spanning trees, Surface order large deviations for Ising, Potts and percolation models

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Correlation inequalities on some partially ordered sets
• Strict inequality for critical values of Potts models and random-cluster processes
• On a combinatorial conjecture concerning disjoint occurrences of events
• Potts models and random-cluster processes with many-body interactions
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Percolation Processes: Lower Bounds for the Critical Probability
• Inequalities with applications to percolation and reliability
• Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its Subgraphs