| Autor: |
van Rensburg, EJ Janse, Whittington, SG |
| Rok vydání: |
2024 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We investigate a lattice model of comb polymers and derive bounds on the exponential growth rate of the number of embeddings of the comb. A comb is composed of a backbone that is a self-avoiding walk and a set of $t$ teeth, also modelled as mutually and self-avoiding walks, attached to the backbone at vertices or nodes of degree 3. Each tooth of the comb has $m_a$ edges and there are $m_b$ edges in the backbone between adjacent degree 3 vertices and between the first and last nodes of degree 3 and the end vertices of degree 1 of the backbone. We are interested in the exponential growth rate as $t \to \infty$ with $m_a$ and $m_b$ fixed. We prove upper bounds on this growth rate and show that for small values of $m_a$ the growth rate is strictly less than that of self-avoiding walks. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
