Abstract
A recently developed model of random walks on a D-dimensional hyperspherical lattice, where D is not restricted to integer values, is used to study polymer growth near a D-dimensional attractive hyperspherical boundary. The model determines the fraction P(κ) of the polymer adsorbed on this boundary as a function of the attractive potential κ for all values of D. The adsorption fraction P(κ) exhibits a second-order phase transition with a universal, nontrivial scaling coefficient for 0<D<4, D≠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 2, where P(κ) scales linearly and exponentially, respectively. A crossover transition that depends on the radius of the adsorbing boundary is found. © 1996 The American Physical Society.
- Received 8 February 1996
DOI:https://doi.org/10.1103/PhysRevE.54.127
©1996 American Physical Society