Abstract
Let ζl be the critical exponent associated with the probability that l independent N-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ζ2=0.6240±0.0005±0.0011 and ζ3=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ζ2=5/8 and ζ3=35/24.
Original language | English (US) |
---|---|
Pages (from-to) | 723-748 |
Number of pages | 26 |
Journal | Journal of Statistical Physics |
Volume | 61 |
Issue number | 3-4 |
DOIs | |
State | Published - Nov 1990 |
Keywords
- Monte Carlo
- conformal invariance
- maximum-likelihood estimation
- mutually-avoiding walks
- random walk
- self-avoiding walk
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics