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.
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Gherardi, M. Exact Sampling of Self-avoiding Paths via Discrete Schramm-Loewner Evolution. J Stat Phys 140, 1115–1129 (2010). https://doi.org/10.1007/s10955-010-0031-8
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DOI: https://doi.org/10.1007/s10955-010-0031-8