2013/02/28 by Nathan Clisby
Materials Science · Mathematics · Physics and Astronomy · #Amplitude #Computer science #Constant (computer programming) #Exponent #Exponential function #Exponential growth #Material Dynamics and Properties #Mathematical analysis #Mathematics #Physics #Power law #Quantum mechanics #Random walk #Scaling #Self-avoiding walk #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8113/46/23/235001
published as J. Phys. A: Math. Theor. 46, 235001 (2013) · 26 pages, 19 figures; typos fixed, expanded arguments for $γ$ and $ν$, added explanation for absence of analytic corrections to scaling, changed conclusion about existence of anti-ferromagnetic singularity, and added an example of a knotted endless self-avoiding walk
arxiv created 2013/03/13 · openalex publication_date 2013/05/16 · arxiv updated 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a self-avoiding walk model for which end-effects are completely eliminated. We enumerate the number of these walks for various lattices in dimensions two and three, and use these enumerations to study the properties of this model. We find that endless self-avoiding walks have the same connective constant as self-avoiding walks, and the same Flory exponent ν. However, there is no power law correction to the exponential number growth for this new model, i.e. the critical exponent γ = 1 exactly in any dimension. In addition, the number growth has no analytic corrections to scaling, and we have convincing numerical evidence to support the conjecture that the amplitude for the number growth is a universal quantity. The technique by which end-effects are eliminated may be generalized to other models of polymers such as interacting self-avoiding walks.