Article révisé par les pairs
| Résumé : | Following critical suggestions made by Mazur and Rubin our exact data for the average span 〈dn〉 of self-avoiding walks on various two- and three-dimensional lattices are reanalyzed by the so-called ratio method, assuming that, for large n, 〈dn〉 + 1 ∼ nδ (1 + a/n + ⋯) instead of 〈dn〉 ∼ nδ (1 + a/n + ⋯) as previously. Using thisnew asymptotic form one finds δ = 1 2γ both in two and three dimensions (within the limit of uncertainties of the required extrapolations) where γ is the characteristic exponent of the mean-square, end-to-end distance, i.e., 〈r2n〉 ∼ nγ (γ = 3 2 in two dimensions and 6 5 in three dimensions). Although objective arguments in support of the new asymptotic form are slight, the plausibility of the results it leads to seems to be a reasonable plea in its favour: no new exponent should then be introduced for describing the behaviour of the span at large n values. © 1974. |
