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

Abstract

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${}_{8/3}$.

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

Cited by in corpus (30)

• 2D growth processes: SLE and Loewner chains
• A Guide to Stochastic Loewner Evolution and its Applications
• Random planar curves and Schramm-Loewner evolutions
• Winding angle variance of Fortuin-Kasteleyn contours
• Conformal Invariance and Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk - Monte Carlo Tests
• Watersheds are Schramm-Loewner Evolution curves
• Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface
• Direct Evidence for Conformal Invariance of Avalanche Frontier in Sandpile Models
• Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface
• The self-avoiding walk in a strip
• Area distribution of the planar random loop boundary
• On Connections of Conformal Field Theory and Stochastic Lœwner Evolution
• The Length of an SLE - Monte Carlo Studies
• First passage times and distances along critical curves
• Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves
• Theta-point polymers in the plane and Schramm-Loewner evolution
• Conformal restriction and related questions
• Conformal invariance of the 3D self-avoiding walk
• The Exit Distribution for Smart Kinetic Walk with Symmetric and Asymmetric Transition Probability
• Loop erased random walk on a percolation cluster is compatible with Schramm-Loewner evolution
• q-deformed Loewner evolution
• A series test of the scaling limit of self-avoiding walks
• Transforming fixed-length self-avoiding walks into radial SLE_8/3
• Urn models, Markov chains and random walks in cosmological topologically massive gravity at the critical point
• Conformal fields, restriction properties, degenerate representations and SLE
• A non-intersecting random walk on the Manhattan lattice and SLE_6
• Intersection probabilities for a chordal SLE path and a semicircle
• $SLE(\kappa ,\rho )$ processes, hiding exponents and self-avoiding walks in a wedge
• Stochastic Loewner Evolution
• Numerical evaluation of the Gauss hypergeometric function: Implementation and application to Schramm-Loewner evolution