Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk

Details Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk

2001-12-21

arxiv.org/abs/math/0112246v1

Phys. Rev. Lett. 88, 130601 (2002)

Mathematics

Probability

TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated postscript)

Scientific paper

10.1103/PhysRevLett.88.130601

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of these predictions is that they yield not just critical exponents, but probability distributions for certain random variables associated with the self-avoiding walk. We test two of these predictions with Monte Carlo simulations and find excellent agreement, thus providing numerical support to the conjecture that the scaling limit of the SAW is SLE$_{8/3}$.

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