Abstract
We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind⩾2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd→∞.
Similar content being viewed by others
References
S. B. Lee and H. Nakanishi,Phys. Rev. B 33:1953 (1986).
V. Privman and S. Redner,Z. Phys. B 67:129 (1987).
J. J. G. Molina and J. G. de la Torre,J. Chem. Phys. 84:4026 (1986).
V. Privman and H. L. Frisch,J. Chem. Phys. (1988), in press.
H. Nakanishi, preprint (1987).
S. Redner and I. Majid,J. Phys. A 16:L307 (1983).
J. L. Cardy,J. Phys. A 16:L355 (1983).
A. M. Szpilka,J. Phys. A 16:2883 (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Privman, V., Švrakić, N.M. Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks. J Stat Phys 50, 81–89 (1988). https://doi.org/10.1007/BF01022988
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01022988