Resistance and spectral dimension of self-avoiding walks with local bridges.

摘要: Self-avoiding-walk (SAW) configurations are considered by incorporating local bridges, i.e., connecting any two nearest-neighbor sites visited the SAW massless cross links. Introducing a new elegant method of estimating resistance an arbitrary network, we find exponent \ensuremath{\delta}=0.920\ifmmode\pm\else\textpm\fi{}0.005 in d=2 enumerating random samples SAW's using Monte Carlo method. We also shortest-connecting-path-length t to be equal 0.975\ifmmode\pm\else\textpm\fi{}0.005 simulation technique dimension. Random walks on networks with bridges studied scaling formalism ``grand canonical ensemble'' picture SAW's. fit mean end-to-end distance 〈${R}_{t}$〉 steps form 〈${R}_{t}$〉\ensuremath{\sim}${t}^{1}$/${d}_{w}$F((f-${f}_{c}$)${t}^{x}$) (f being fugacity SAW's) and ${d}_{w}$=${d}_{F}$(1+\ensuremath{\delta}). In dimensions this predicts spectral dimension ${d}_{S}$ (=2${d}_{F}$/${d}_{w}$) 1.042.