Hyperscaling for polymer rings |
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Authors: | Bertrand Duplantier |
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Affiliation: | CEA, Service de Physique Théorique, CE Saclay, F-91191, Gif-sur-Yvette Cedex, France |
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Abstract: | The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a d-dimensional lattice obeys hyperscaling. The combination pNR2Nd/2μ−N (where pN is the number of configurations of an oriented and rooted N-step ring, R2N a typical average size squared, and μ the SAW effective connectivity constant of the lattice) is equal for N å ∞ to a lattice-dependent constant times a universal amplitude A(d). The latter amplitude is calculated directly from the minimal continous Edwards model to second order in 4 − d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculations, and former simulations. As a consequence, we show that the universal constant λ appearing to second order in in all critical phenomena amplitude ratios is equal to . |
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