Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution

Details Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution Exact sampling of self-avoiding paths via discrete Schramm-Loewner evolution

2010-03-15

arxiv.org/abs/1003.2909v2

J. Stat. Phys. (2010) 140, 6

Physics

Condensed Matter

Statistical Mechanics

18 pages, 4 figures. Some sections rewritten (including title and abstract), numerical results added, references added. Accept

Scientific paper

10.1007/s10955-010-0031-8

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.

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