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arXiv · hep-lat/9506013

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

Carl M. Bender·Peter N. Meisinger·Stefan Boettcher
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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 $P(κ)$ 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 nontrivial scaling coefficient for $0 4$. At $D=4$ there is a tricritical point with logarithmic scaling. This model reproduces earlier results for $D=1$ and $D=2$, where $P(κ)$ scales linearly and exponentially, respectively. A crossover transition that depends on the radius of the adsorbing boundary is found.

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Carl M. Bender, Peter N. Meisinger, Stefan Boettcher. 1995-06-06. SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A HYPERSPHERICAL BOUNDARY. https://doi.org/10.1103/physreve.54.127

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