Statistical Models on Spherical Geometries

S. Boettcher, M. Moshe
1995 Physical Review Letters  
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
more » ... l cell membrane. We find that the fraction of adsorbed monomers on the boundary vanishes exponentially when the adsorption energy decreases towards its critical value.
doi:10.1103/physrevlett.74.2410 pmid:10057921 fatcat:ppdp7kzr6zebxcw5pjkxdfdlnu