Scaling of Self-Avoiding Walks and Self-Avoiding Trails in Three Dimensions

Abstract

Motivated by recent claims of a proof that the length scale exponent for the end-to-end distance scaling of self-avoiding walks is precisely $7/12=\mathrm{0.5833...}$, we present results of large-scale simulations of self-avoiding walks and self-avoiding trails with repulsive contact interactions on the hypercubic lattice. We find no evidence to support this claim; our estimate $\nu =0.5874(2)$ is in accord with the best previous results from simulations.

References in corpus (1)

• Scaling of Self-Avoiding Walks in High Dimensions

Cited by in corpus (21)

• 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
• Polymers Confined between Two Parallel Plane Walls
• Virial coefficients and osmotic pressure in polymer solutions in good-solvent conditions
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"
• On the location of the surface-attached globule phase in collapsing polymers
• Exact enumeration of self-avoiding walks on BCC and FCC lattices
• Universality of crossover scaling for the adsorption transition of lattice polymers
• Polymer size in dilute solutions in the good-solvent regime
• Exact and Monte Carlo study of adsorption of a self-interacting polymer chain for a family of three-dimensional fractals
• Two-parameter model predictions and theta-point crossover for linear-polymer solutions
• Renormalised four-point coupling constant in the three-dimensional O(N) model with N=0
• Third-harmonic exponent in three-dimensional N-vector models
• Universal shape ratios for polymers grafted at a flat surface
• Anomalous critical behaviour in the polymer collapse transition of three-dimensional lattice trails
• Pseudo-First-Order Transition in Interacting Self-avoiding Walks and Trails
• Corrections to scaling in multicomponent polymer solutions
• Monte Carlo Investigation of Lattice Models of Polymer Collapse in Five Dimensions
• Structural characterization of ice polymorphs from self-avoiding walks
• On the number of contacts of a floating polymer chain cross-linked with a surface adsorbed chain on fractal structures