Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk

From MaRDI portal
Publication:960150

DOI10.1007/s10955-008-9580-5zbMath1152.82007arXiv0712.0312OpenAlexW3100355816MaRDI QIDQ960150

Markus Heydenreich, Akira Sakai, Remco van der Hofstad

Publication date: 16 December 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0312




Related Items (33)

Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on ZdApplicability of \(n\)-vicinity method for calculation of free energy of Ising modelSpatial networks and percolation. Abstracts from the workshop held January 17--23, 2021 (hybrid meeting)Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlationCorrect bounds on the Ising lace-expansion coefficientsOn the derivation of mean-field percolation critical exponents from the triangle conditionThe survival probability and \(r\)-point functions in high dimensionsCritical site percolation in high dimensionScale-free percolationRandom walk on barely supercritical branching random walkGeneralized approach to the non-backtracking lace expansionThe critical two-point function for long-range percolation on the hierarchical latticeHigh-dimensional near-critical percolation and the torus plateauLong-range self-avoiding walk converges to \(\alpha\)-stable processesThe triangle and the open triangleAsymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolationThe discontinuity of the specific heat for the 5D Ising modelCritical two-point function for long-range \(O(n)\) models below the upper critical dimensionCritical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimensionPercolation on a product of two treesArm exponents in high dimensional percolationMean-Field Bound on the 1-Arm Exponent for Ising Ferromagnets in High DimensionsLace expansion for the Ising modelRandom walk on the high-dimensional IICScaling limits and critical behaviour of the 4-dimensional \(n\)-component \(|\varphi|^4\) spin modelRandom currents and continuity of Ising model's spontaneous magnetizationCritical 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 \(\varphi^4\) modelHigh-dimensional incipient infinite clusters revisitedPower-law bounds for critical long-range percolation below the upper-critical dimensionThe Alexander-Orbach conjecture holds in high dimensionsSelf-avoiding walk, spin systems and renormalizationCritical two-point functions for long-range statistical-mechanical models in high dimensions



Cites Work


This page was built for publication: Mean-field behavior for long- and finite range Ising model, percolation and self-avoiding walk