SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A HYPERSPHERICAL BOUNDARY

Abstract

A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The model determines the fraction $P(\kappa )$ of the polymer adsorbed on this boundary as a function of the attractive potential $\kappa$ for all values of $D$. The adsorption fraction $P(\kappa )$ exhibits a second-order phase transition with a nontrivial scaling coefficient for $0<D<4$, $D\ne 2$, and exhibits a first-order phase transition for $D>4$. At $D=4$ there is a tricritical point with logarithmic scaling. This model reproduces earlier results for $D=1$ and $D=2$, where $P(\kappa )$ scales linearly and exponentially, respectively. A crossover transition that depends on the radius of the adsorbing boundary is found.

20 pages, Revtex, uuencoded, (two ps-figures included, fig2 in color)

References in corpus (8)

• Random Walks in Noninteger Dimension
• Spherically-Symmetric Random Walks in Noninteger Dimension
• Statistical Models on Spherical Geometries
• Universality in Random Walk Models with Birth and Death
• Polymer-Chain Adsorption Transition at a Cylindrical Boundary
• SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF ORTHOGONAL POLYNOMIALS
• SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR
• Random Walk Model on a Hyper-Spherical Lattice

Cited by in corpus (2)

• SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF ORTHOGONAL POLYNOMIALS
• SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL BEHAVIOR