Compressed self-avoiding walks, bridges and polygons

Abstract

We study various self-avoiding walks (SAWs) which are constrained to lie in the upper half-plane and are subjected to a compressive force. This force is applied to the vertex or vertices of the walk located at the maximum distance above the boundary of the half-space. In the case of bridges, this is the unique end-point. In the case of SAWs or self-avoiding polygons, this corresponds to all vertices of maximal height. We first use the conjectured relation with the Schramm-Loewner evolution to predict the form of the partition function including the values of the exponents, and then we use series analysis to test these predictions.

29 pages, 6 figures

References in corpus (2)

• Accurate estimate of the critical exponent $\nu$ for self-avoiding walks via a fast implementation of the pivot algorithm
• Compressed self-avoiding walks, bridges and polygons

Cited by in corpus (15)

• Compressed self-avoiding walks, bridges and polygons
• Series extension: Predicting approximate series coefficients from a finite number of exact coefficients
• Three-dimensional terminally attached self-avoiding walks and bridges
• Compacted binary trees admit a stretched exponential
• Self-avoiding walks subject to a force
• Polygons in restricted geometries subjected to infinite forces
• Polygons pulled from an adsorbing surface
• Force-induced desorption of uniform branched polymers
• Self-avoiding walks adsorbed at a surface and subject to a force
• Two-dimensional interacting self-avoiding walks: new estimates for critical temperatures and exponents
• Adsorbing staircase polygons subject to a force
• Force-induced desorption of $3$-star polymers: a self-avoiding walk model
• Force-induced desorption of uniform block copolymers
• Numerical studies of Thompson's group F and related groups
• Exactly Solved Models and Beyond: a special issue in honour of R J Baxter's 75th birthday