Power-law corrections to exponential decay of connectivities and correlations in lattice models.

DOI10.1214/aop/1008956323zbMath1034.82005OpenAlexW1602285629MaRDI QIDQ1872177

Kenneth S. Alexander

Publication date: 6 May 2003

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1008956323

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

Ornstein-Zernike theory for the Bernoulli bond percolation on \(\mathbb Z^d\) ⋮ Mixing properties and exponential decay for lattice systems in finite volumes. ⋮ Lower bounds for boundary roughness for droplets in Bernoulli percolation

Cites Work

• Gaussian fluctuations of connectivities in the subcritical regime of percolation
• Statistical mechanical methods in particle structure analysis of lattice field theories. II. Scalar and surface models
• The Wulff construction and asymptotics of the finite cluster distribution for two-dimensional Bernoulli percolation
• Stability of the Wulff minimum and fluctuations in shape for large finite clusters in two-dimensional percolation
• Approximation of subadditive functions and convergence rates in limiting-shape results
• Large deviations and continuum limit in the 2D Ising model
• On weak mixing in lattice models
• Ornstein-Zernike theory for the Bernoulli bond percolation on \(\mathbb Z^d\)
• 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.
• Lower bounds on the connectivity function in all directions for Bernoulli percolation in two and three dimensions
• Inequalities with applications to percolation and reliability
• The asymmetric random cluster model and comparison of Ising and Potts models
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item