Exact Potts/Tutte Polynomials for Hammock Chain Graphs
| Autor: | Chen, Yue, Shrock, Robert |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We present exact calculations of the $q$-state Potts model partition functions and the equivalent Tutte polynomials for chain graphs comprised of $m$ repeated hammock subgraphs $H_{e_1,...,e_r}$ connected with line graphs of length $e_g$ edges, such that the chains have open or cyclic boundary conditions (BC). Here, $H_{e_1,...,e_r}$ is a hammock (series-parallel) subgraph with $r$ separate paths along ``ropes'' with respective lengths $e_1, ..., e_r$ edges, connecting the two end vertices. We denote the resultant chain graph as $G_{\{e_1,...,e_r\},e_g,m;BC}$. We discuss special cases, including chromatic, flow, and reliability polynomials. In the case of cyclic boundary conditions, the zeros of the Potts partition function in the complex $q$ function accumulate, in the limit $m \to \infty$, onto curves forming a locus ${\cal B}$, and we study this locus. Comment: 57 pages, latex, 26 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|