New upper bound for the connective constant for square-lattice self-avoiding walks

TL;DR

This paper improves the upper bound for the connective constant of self-avoiding walks on the square lattice by refining automaton methods and analyzing loops up to length 26.

Contribution

It introduces a modified automaton approach and considers longer loops to tighten the upper bound for the connective constant.

Findings

Upper bound for the connective constant is 2.662343.

Automaton modification enhances bound accuracy.

Considering loops up to length 26 improves previous estimates.

Abstract

By modifying the automaton used by P{\"o}nitz and Tittman [4], and considering loops of length up to 26, we obtain 2.662343 as an upper bound for the connective constant in the lattice Z 2 .