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arXiv · hep-lat/9502010

Statistical Models on Spherical Geometries

S. Boettcher·M. Moshe
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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 a 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.

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BibTeXRIS

S. Boettcher, M. Moshe. 1995-02-15. Statistical Models on Spherical Geometries. https://doi.org/10.1103/physrevlett.74.2410

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