Modified self-avoiding walk in a polymerization process

The modified SAW (mSAW) is defined as a statistical method to treat a polymerization process in a manner similar to that used to treat chains with excluded volume statistics where no two monomers can occupy the same site in space. Unlike the chains with excluded volume statistics, the walk algorithm does not terminate when the next walk is an occupied site. Instead the walker continues along a different direction, Monte Carlo simulations of the random walk are carried out on both 2D and 3D lattices. Universality classes different from those of the chain with excluded volume statistics are found. The critical exponents of the mean-square end-to-end distance are found to be 1.437 (0.005) for 2D and 1.007 (0.004) for 3D, where the figures in the parentheses are the uncertainties of the last digit. The universality classes are determined from rigorous computer simulations.