The pivot algorithm: A highly efficient Monte Carlo method for the selfavoiding walk
Abstract
The pivot algorithm is a dynamic Monte Carlo algorithm, first invented by Lal, which generates selfavoiding walks (SAWs) in a canonical (fixed N) ensemble with free endpoints (here N is the number of steps in the walk). We find that the pivot algorithm is extraordinarily efficient: one "effectively independent" sample can be produced in a computer time of order N. This paper is a comprehensive study of the pivot algorithm, including: a heuristic and numerical analysis of the acceptance fraction and autocorrelation time; an exact analysis of the pivot algorithm for ordinary random walk; a discussion of data structures and computational complexity; a rigorous proof of ergodicity; and numerical results on selfavoiding walks in two and three dimensions. Our estimates for critical exponents are υ=0.7496±0.0007 in d=2 and υ= 0.592±0.003 in d=3 (95% confidence limits), based on SAWs of lengths 200⩽ N⩽10000 and 200⩽ N⩽ 3000, respectively.
 Publication:

Journal of Statistical Physics
 Pub Date:
 January 1988
 DOI:
 10.1007/BF01022990
 Bibcode:
 1988JSP....50..109M
 Keywords:

 Selfavoiding walk;
 polymer;
 Monte Carlo;
 pivot algorithm;
 critical exponent