J. Phys. I France
Volume 3, Numéro 4, April 1993
Page(s) 925 - 934
DOI: 10.1051/jp1:1993173
J. Phys. I France 3 (1993) 925-934

Surface geometry and local critical behaviour : the self-avoiding-walk

Loïc Turban and Bertrand Berche

Laboratoire de Physique du Solide, Université de Nancy I, BP 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France

(Received 21 October 1992, accepted 27 November 1992)

The statistics of a polymer chain confined inside a system which is limited by a parabolic-like surface $v = \pm Cu^k$ is studied through Monte-Carlo simulations in two dimensions. In agreement with scaling considerations, the surface geometry is found to be a relevant perturbation to the flat surface behaviour when the shape exponent k is smaller than one. In this case the system becomes anisotropic with a radius exponent $v^p_{\parallel}$ along the parabola greater than the exponent $v^p_{\perp}$ in the transverse direction. When k < 1 the anisotropy ratio z adjusts itself to the value k-1 for which the surface geometry is a marginal perturbation. The exponents obtained analytically, using either the blob picture approach or a Flory approximation, are in good agreement with the 2d simulation results.


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