HYPERSCALING FOR POLYMER RINGS

Authors
Citation
B. Duplantier, HYPERSCALING FOR POLYMER RINGS, Nuclear physics. B, 430(3), 1994, pp. 489-533
Citations number
51
Categorie Soggetti
Physics, Nuclear
Journal title
ISSN journal
05503213
Volume
430
Issue
3
Year of publication
1994
Pages
489 - 533
Database
ISI
SICI code
0550-3213(1994)430:3<489:HFPR>2.0.ZU;2-N
Abstract
The statistics of a long closed self-avoiding walk (SAW) or polymer ri ng on a d-dimensional lattice obeys hyperscaling. The combination p(N) [R(2)](d/2)(N)mu(-N) (where p(N) is the number of configurations of a n oriented and rooted N-step ring, [R(2)](N) a typical average size sq uared, and mu the SAW effective connectivity constant of the lattice) is equal for N --> infinity to a lattice-dependent constant times a un iversal amplitude A(d). The latter amplitude is calculated directly fr om the minimal continuous Edwards model to second order in epsilon = 4 - d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculation s, and former simulations. As a consequence, we show that the universa l constant lambda appearing to second order in epsilon in all critical phenomena amplitude ratios is equal to lambda = 1/3 psi'(1/3)-2/9 pi( 2).