Related Experiment Video
Updated: Jul 17, 2026

Rendering SiO2/Si Surfaces Omniphobic by Carving Gas-Entrapping Microtextures Comprising Reentrant and Doubly Reentrant Cavities or Pillars
Published on: February 11, 2020
Violation of the des Cloizeaux relation for self-avoiding walks on Sierpinski square lattices
Francesco Marini1, Anke Ordemann, Markus Porto
1Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy.
Abstract:
The statistics of self-avoiding walks (SAWs) on deterministic fractal structures with infinite ramification, modeled by Sierpinski square lattices, is revisited in two and three dimensions using the reptation algorithm. The probability distribution function of the end-to-end distance of SAWs, consisting of up to 400 steps, is obtained and its scaling behavior at small distances is studied. The resulting scaling exponents are confronted with previous calculations for much shorter linear chains (20 to 30 steps) based on the exact enumeration (EE) technique. The present results coincide with the EE values in two dimensions, but differ slightly in three dimensions. A possible explanation for this discrepancy is discussed. Despite this, the violation of the so-called des Cloizeaux relation, a renormalization result that holds on regular lattices and on deterministic fractal structures with finite ramification, is confirmed numerically.
Related Concept Videos
Saint-Venant's Principle
Lattice Centering and Coordination Number
Types of Unit Cells
Imagine taking a large number of identical...
Bewley Lattice Diagram
Green’s Theorem
Extended Versions of Green’s Theorem
Castigliano's Theorem: Problem Solving

