A quantum N-dimer model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914246880657408 |
|---|---|
| author | Douglas, Daniel C. Kenyon, Richard Ovenhouse, Nicholas Panitch, Samuel Tata, Sri |
| author_facet | Douglas, Daniel C. Kenyon, Richard Ovenhouse, Nicholas Panitch, Samuel Tata, Sri |
| contents | We study a quantum version of the $n$-dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in particular, can be used to construct the Jones polynomial of a knot in $\mathbb{R}^3$). We apply this machinery to construct an isotopy invariant polynomial for knotted bipartite ribbon graphs in $\mathbb{R}^3$, giving, in the planar setting, a quantum $n$-dimer partition function. As one application, we compute the expected number of loops in the (classical) double dimer model for planar bipartite graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantum N-dimer model Douglas, Daniel C. Kenyon, Richard Ovenhouse, Nicholas Panitch, Samuel Tata, Sri Quantum Algebra Combinatorics Geometric Topology 05E10, 57K31, 82B20 We study a quantum version of the $n$-dimer model from statistical mechanics, based on the formalism from quantum topology developed by Reshetikhin and Turaev (the latter which, in particular, can be used to construct the Jones polynomial of a knot in $\mathbb{R}^3$). We apply this machinery to construct an isotopy invariant polynomial for knotted bipartite ribbon graphs in $\mathbb{R}^3$, giving, in the planar setting, a quantum $n$-dimer partition function. As one application, we compute the expected number of loops in the (classical) double dimer model for planar bipartite graphs. |
| title | A quantum N-dimer model |
| topic | Quantum Algebra Combinatorics Geometric Topology 05E10, 57K31, 82B20 |
| url | https://arxiv.org/abs/2510.07543 |