Loop-erased self-avoiding random walks in four and five dimensions

Abstract

Monte Carlo simulations of loop-erased self-avoiding random walks in four and five dimensions were performed, using two distinct algorithms. We find consistency between these methods in their estimates of critical exponents. The upper critical dimension for this phenomenon is four, and it has been shown that the mean square end-to-end distance grows as n(log n)α. It has recently been established that the mean square end-to-end distance is asymptotically bounded by n(log n)1/3 (see Ref. 21). Our results show that asymptotic convergence to n(log n)1/3 in fact obtains and does so rather quickly. In five dimensions we examine the rate of asymptotic convergence to the mean-field model. © 1996 by John Wiley & Sons, Inc.