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Monte Carlo simulations of self-avoiding walks on the percolation cluster (SAWS ON FRACTAL)
Start date: 01 Aug 2007, End date: 31 Jul 2008 PROJECT  FINISHED 

The scaling properties of long flexible polymer chains in good solvent are perfectly described within a model of a self-avoiding walk (SAW) on a regular lattice. The question of a great interest is the influence of the structural disorder of the lattice on the universal properties of a SAW. In the given project, we will be interested in the special case, when disordered lattice is exactly at the percolation threshold so that the SAW is allowed to have its steps only on the percolation cluster, having the fr actal structure. Up to date there exists not many works dedicated to Monte Carlo (MC) simulations of our problem and they are unfortunately far from the state-of-the-art calculations. In the intended research we plan to perform the MC simulations of a SAW on the percolation clusters for d=2,3,4,5-dimensional lattices to find the numerical values of the critical exponents, governing its universal properties. In this way we will complete the set of theoretical and exact enumeration estimates by the MC result.
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