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arXiv · hep-lat/9410020

Random Walk Model on a Hyper-Spherical Lattice

S. Boettcher
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Abstract

We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram of a percolation problem. We find a line of second and first order phase transitions separated by a tricritical point. Then, we analyze the adsorption-desorption transition for a polymer growing near the attractive boundary of a cylindrical cell membrane. We find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value. We observe a crossover phenomenon to an area of linear growth at energies of the order of the inverse cell radius.

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S. Boettcher. 1994-10-26. Random Walk Model on a Hyper-Spherical Lattice. https://doi.org/10.1016/0920-5632(95)00418-9

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