SURFACE GEOMETRY AND LOCAL CRITICAL-BEHAVIOR - THE SELF-AVOIDING-WALK

The statistics of a polymer chain confined inside a system which is li mited by a parabolic-like surface v = +/- Cu(k) is studied through Mon te-Carlo simulations in two dimensions. In agreement with scaling cons iderations, the surface geometry is found to be a relevant perturbatio n to the flat surface behaviour when the shape exponent k is smaller t han one. In this case the system becomes anisotropic with a radius exp onent nu(parallel-to)p along the parabola greater than the exponent nu (perpendicular-to)p in the transverse direction. When k < 1 the anisot ropy ratio z adjusts itself to the value k-1 for which the surface geo metry 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.