Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models

DOI10.1214/21-ECP390zbMath1482.82007arXiv2007.00116MaRDI QIDQ2064874

Yacine Aoun

Publication date: 6 January 2022

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.00116

zbMATH Keywords

percolationIsing modelPotts modelstatistical mechanicsprobability theoryrandom-cluster modellong-range

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (2)

Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd ⋮ On the two-point function of the Potts model in the saturation regime

Cites Work

• Random-cluster representation of the Ashkin-Teller model
• Decay of the two-point function in one-dimensional \(\text{O}(N)\) spin models with long-range interactions.
• Sharp phase transition for the random-cluster and Potts models via decision trees
• The sharp phase transition for level set percolation of smooth planar Gaussian fields
• Subcritical phase of \(d\)-dimensional Poisson-Boolean percolation and its vacant set
• Decay properties of the connectivity for mixed long range percolation models on \(\mathbb Z^{d}\)
• Lectures on the Ising and Potts Models on the Hypercubic Lattice
• Statistical Mechanics of Lattice Systems
• The Random-Cluster Model

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