Department of Physics Papers

Document Type

Journal Article

Date of this Version

5-1-1990

Publication Source

Physical Review B

Volume

41

Issue

13

Start Page

9183

Last Page

9206

DOI

10.1103/PhysRevB.41.9183

Abstract

Series expansions for general moments of the bond-percolation cluster-size distribution on hypercubic lattices to 15th order in the concentration have been obtained. This is one more than the previously published series for the mean cluster size in three dimensions and four terms more for higher moments and higher dimensions. Critical exponents, amplitude ratios, and thresholds have been calculated from these and other series by a variety of independent analysis techniques. A comprehensive summary of extant estimates for exponents, some universal amplitude ratios, and thresholds for percolation in all dimensions is given, and our results are shown to be in excellent agreement with the ε expansion and some of the most accurate simulation estimates. We obtain threshold values of 0.2488±0.0002 and 0.180 25±0.000 15 for the three-dimensional bond problem on the simple-cubic and body-centered-cubic lattices, respectively, and 0.160 05±0.000 15 and 0.118 19±0.000 04, for the hypercubic bond problem in four and five dimensions, respectively. Our direct exponent estimates are γ=1.805±0.02, 1.435±0.015, and 1.185±0.005, and β=0.405±0.025, 0.639±0.020, and 0.835±0.005 in three, four, and five dimensions, respectively.

Comments

At the time of publication, author A. Brooks Harris was also affiliated with Tel Aviv University. Currently, he is a faculty member in the Physics Department at the University of Pennsylvania.

Included in

Physics Commons

Share

COinS
 

Date Posted: 12 August 2015

This document has been peer reviewed.