Monte Carlo methods for the self-avoiding walk

Conformal Invariance and Stochastic Loewner Evolution Predictions for the 2D Self-Avoiding Walk - Monte Carlo Tests

Simulations of the self-avoiding walk (SAW) are performed in a half-plane and a cutplane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm and Werner that the scaling limit of the two-dimensional SAW is given by Schramm’s Stochastic Loewner Evolution (SLE). The agreement is found to be excellent. The simulations also tes...

Monte Carlo comparisons of the self-avoiding walk and SLE as parameterized curves

The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter κ equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has a standard parameterization using the half-plane capacity. These two parameterizations do not correspond with one another. To make the scaling limit of the SAW a...

A Monte Carlo study of non-trapped self-avoiding walks

In this paper, we study non-trapped self-avoiding walks, which are selfavoiding walks which can be extended to an infinite length. We apply the flatPERM Monte Carlo method for this purpose, generating non-trapped SAWs of length up to 1024 on the square, triangular and hexagonal lattices, and calculating their number and mean squared end-to-end distance. We find strong evidence that the growth c...

he p - la t / 9 50 90 32 12 S ep 1 99 5 1 Monte Carlo methods for the self - avoiding walk

Monte Carlo and quasi-Monte Carlo methods

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...