Abstract
We introduce a new Monte Carlo algorithm for generating self-avoiding walks of variable length and free endpoints. The algorithm works in the unorthodox ensemble consisting of all pairs of SAWs such that the total number of steps Ntot in the two walks is fixed. The elementary moves of the algorithm are fixed-N (e.g., pivot) moves on the individual walks, and a novel "join- and-cut" move that concatenates the two walks and then cuts them at a random location. We analyze the dynamic critical behavior of the new algorithm, using a combination of rigorous, heuristic, and numerical methods. In two dimensions the autocorrelation time in CPU units grows as N≈1.5, and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent γ.
Original language | English (US) |
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Pages (from-to) | 65-111 |
Number of pages | 47 |
Journal | Journal of Statistical Physics |
Volume | 67 |
Issue number | 1-2 |
DOIs | |
State | Published - Apr 1992 |
Keywords
- Monte Carlo
- Self-avoiding walk
- critical exponent
- join- and-cut algorithm
- pivot algorithm
- polymer
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics