Critical two-point functions for long-range statistical-mechanical models in high dimensions

DOI10.1214/13-AOP843zbMath1342.60162arXiv1204.1180OpenAlexW3101804231MaRDI QIDQ2338912

Akira Sakai, Lung-Chi Chen

Publication date: 27 March 2015

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

Full work available at URL: https://arxiv.org/abs/1204.1180

zbMATH Keywords

percolationIsing modeltwo-point functioncritical behaviorlace expansionself-avoiding walklong-range random walk

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items

Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on Zd, Spatial networks and percolation. Abstracts from the workshop held January 17--23, 2021 (hybrid meeting), Lace expansion for dummies, Correct bounds on the Ising lace-expansion coefficients, On the derivation of mean-field percolation critical exponents from the triangle condition, Random walk on barely supercritical branching random walk, The critical two-point function for long-range percolation on the hierarchical lattice, Decay of the Green's function of the fractional Anderson model and connection to long-range SAW, High-dimensional near-critical percolation and the torus plateau, Critical two-point function for long-range \(O(n)\) models below the upper critical dimension, Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension, Mean-Field Bound on the 1-Arm Exponent for Ising Ferromagnets in High Dimensions, Random walk on the high-dimensional IIC, Random currents and continuity of Ising model's spontaneous magnetization, Critical two-point function for long-range models with power-law couplings: the marginal case for \({d\ge d_{\mathrm{c}}}\), Application of the lace expansion to the \(\varphi^4\) model, High-dimensional incipient infinite clusters revisited, Power-law bounds for critical long-range percolation below the upper-critical dimension, A simple convergence proof for the lace expansion, Critical two-point function of the 4-dimensional weakly self-avoiding walk

Cites Work

• Unnamed Item
• Unnamed Item
• Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II
• Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
• Mean-field critical behaviour for percolation in high dimensions
• Critical behavior and the limit distribution for long-range oriented percolation. I
• Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk
• Tree graph inequalities and critical behavior in percolation models
• On the critical behavior of the magnetization in high-dimensional Ising models
• Percolation critical exponents under the triangle condition
• A generalised inductive approach to the lace expansion
• Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
• Critical two-point functions and the lace expansion for spread-out high-dimensional percolation and related models.
• Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• Lace expansion for the Ising model
• Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals
• The lace expansion and its application. École d'Été de Probabilités de Saint-Flour XXXIV -- 2004.
• Mean-field behavior for the survival probability and the percolation point-to-surface connectivity
• High-dimensional incipient infinite clusters revisited
• Normal Approximation and Asymptotic Expansions
• Inequalities with applications to percolation and reliability
• Percolation
• Arm exponents in high dimensional percolation