Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution
arXiv:1003.2909 · doi:10.1007/s10955-010-0031-8
Abstract
We present an algorithm, based on the iteration of conformal maps, that produces independent samples of self-avoiding paths in the plane. It is a discrete process approximating radial Schramm-Loewner evolution growing to infinity. We focus on the problem of reproducing the parametrization corresponding to that of lattice models, namely self-avoiding walks on the lattice, and we propose a strategy that gives rise to discrete paths where consecutive points lie an approximately constant distance apart from each other. This new method allows us to tackle two non-trivial features of self-avoiding walks that critically depend on the parametrization: the asphericity of a portion of chain and the correction-to-scaling exponent.
18 pages, 4 figures. Some sections rewritten (including title and abstract), numerical results added, references added. Accepted for publication in J. Stat. Phys
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