JOIN-AND-CUT ALGORITHM FOR SELF-AVOIDING WALKS WITH VARIABLE LENGTH AND FREE END-POINTS

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 N(tot) 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 dimension, the autocorrelation time in CPU units grows as N (almost-equal-to 1.5), and the behavior improves in higher dimensions. This algorithm allows high-precision estimation of the critical exponent gamma.