Statistics of self-avoiding walks on randomly diluted lattice

A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities, disorder configuration ensembles, and walk weighting schemes. These results are analyzed and compared with those previously available. Various subtleties in the calculation and definition of these exponents are discussed. Precise numerical values are given for these exponents in most cases, and many new properties are recognized for them.Comment: 34 pages (+ 12 figures), REVTEX 3.

A study of single polymer conformation models

We study single polymer conformations in terms of self-avoiding walk and flight models that incorporate the excluded-volume effect, stiffness, disorder average, and branching by use of extensive computer simulations. We first investigate behaviors of two extensions of the Levy flight, called the node-avoiding (NALF) and the path-avoiding (PALF) Levy flights focusing on the upper critical dimensions of the NALF. Our Monte Carlo results for the NALF are consistent with predictions of the renormalization group calculations for the corresponding spin model but we observe drastic differences between the NALF and the PALF in lower dimensions. Introducing the excluded-volume effect to the random Levy walk model which treats the straight segment of the Levy flight as a sequence of correlated steps, we then propose the self-avoiding Levy walk (SALW) as a model for very stiff polymers that may contain long straight segments. A Flory-type argument is used to determine the upper critical dimensions and the end-to-end distance exponent of the SALW. We next study the stiff chain conformation in three dimensions in the framework of the persistent self-avoiding walk (PSAW) model whose segment size distribution is exponential in contrast to the power-law for the SALW. The crossover behavior of the end-to-end distance controlled by the excluded-volume effect is examined with special interests to test scaling arguments and to analyze the experimental data on poly-hexyl-isocyanate polymers. The effect of disorder on the conformation of a flexible linear chain is studied in terms of the self-avoiding walk (SAW) on randomly diluted lattices. Using an exact enumeration method we obtain the critical exponents for the SAW on percolation clusters different from those for the SAW on pure lattices. Finally mean sizes of the Gaussian branched polymer are calculated for some deterministic models and their exact solutions are given. An old simulation for branched polymers with fixed branching probability is revisited and the result is reanalyzed for a larger set of parameters in terms of a proposed deterministic model