Monte Carlo study of four-dimensional self-avoiding walks of up to one billion steps

Abstract

We study self-avoiding walks on the four-dimensional hypercubic lattice via Monte Carlo simulations of walks with up to one billion steps. We study the expected logarithmic corrections to scaling, and find convincing evidence in support the scaling form predicted by the renormalization group, with an estimate for the power of the logarithmic factor of 0.2516(14), which is consistent with the predicted value of 1/4. We also characterize the behaviour of the pivot algorithm for sampling four-dimensional self-avoiding walks, and conjecture that the probability of a pivot move being successful for an $N$-step walk is $O([\log N{]}^{-1/4})$.

10 pages, 8 figures

References in corpus (4)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• High-precision estimate of the hydrodynamic radius for self-avoiding walks
• Lectures on Self-Avoiding Walks
• Scale-free Monte Carlo method for calculating the critical exponent $\gamma$ of self-avoiding walks

Cited by in corpus (4)

• Introduction to a renormalisation group method
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Off-lattice and parallel implementations of the pivot algorithm