Statistical Models on Spherical Geometries

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.

8 pages, latex, 2 figures in ps

References in corpus (2)

• Random Walks in Noninteger Dimension
• Spherically-Symmetric Random Walks in Noninteger Dimension

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