Self-avoiding Walks of Lattice Strips

2017/09/22 by Rumen Dangovski, Chavdar Lalov, Dangovski, Rumen +1
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1709.09223

openalex publication_date 2017/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study self-avoiding walks on restricted square lattices, more precisely on the lattice strips ℤ × \-1,0,1\ and ℤ× \-1,0,1,2\. We obtain the value of the connective constant for the ℤ × \-1,0,1\ lattice in a new shorter way and deduce close bounds for the connective constant for the ℤ× \-1,0,1,2\ lattice. Moreover, for both lattice strips we find close lower and upper bounds for the number of SAWs of length n by using the connective constant.

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