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→∞.
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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
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DOI: https://doi.org/10.1007/BF01022988