Universal Amplitude Combinations for Self-Avoiding Walks, Polygons and Trails

TL;DR

This paper derives exact relations for amplitude combinations in self-avoiding walks, polygons, and trails, highlighting lattice-dependent factors, and provides new theoretical and numerical results on amplitude ratios and moments.

Contribution

It introduces exact relations for amplitude combinations, clarifies lattice-dependent factors, and presents new numerical data for various lattices and amplitude ratios.

Findings

Exact relations for amplitude combinations are established.

Lattice-dependent factors are identified and analyzed.

New numerical results for amplitude ratios and polygon area moments are provided.

Abstract

We give exact relations for a number of amplitude combinations that occur in the study of self-avoiding walks, polygons and lattice trails. In particular, we elucidate the lattice-dependent factors which occur in those combinations which are otherwise universal, show how these are modified for oriented lattices, and give new results for amplitude ratios involving even moments of the area of polygons. We also survey numerical results for a wide range of amplitudes on a number of oriented and regular lattices, and provide some new ones.