No CrossRef data available.
Article contents
Spread-out limit of the critical points for lattice trees and lattice animals in dimensions $\boldsymbol{d}\boldsymbol\gt \textbf{8}$
Published online by Cambridge University Press: 20 November 2023
Abstract
A spread-out lattice animal is a finite connected set of edges in $\{\{x,y\}\subset \mathbb{Z}^d\;:\;0\lt \|x-y\|\le L\}$. A lattice tree is a lattice animal with no loops. The best estimate on the critical point $p_{\textrm{c}}$ so far was achieved by Penrose (J. Stat. Phys. 77, 3–15, 1994) : $p_{\textrm{c}}=1/e+O(L^{-2d/7}\log L)$ for both models for all $d\ge 1$. In this paper, we show that $p_{\textrm{c}}=1/e+CL^{-d}+O(L^{-d-1})$ for all $d\gt 8$, where the model-dependent constant $C$ has the random-walk representation
MSC classification
- Type
- Paper
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press