The five-vertex model as a discrete log-gas
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911343180775424 |
|---|---|
| author | Colomo, Filippo Mannatzu, Michelangelo Pronko, Andrei G. |
| author_facet | Colomo, Filippo Mannatzu, Michelangelo Pronko, Andrei G. |
| contents | We consider the five-vertex model on a rectangular domain of the square lattice, with the so-called `scalar-product' boundary conditions. We address the evaluation of the free-energy density of the model in the scaling limit, that is when the number of sites is sent to infinity and the mesh of the lattice to zero, while keeping the size of the domain constant. To this aim, we reformulate the partition function of the model in terms of a discrete log-gas, and study its behaviour in the thermodynamic limit. We reproduce previous results, obtained by using a differential equation approach. Moreover, we provide the explicit form of the resolvent in all possible regimes. This work is preliminary to further studies of limit shape phenomena in the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The five-vertex model as a discrete log-gas Colomo, Filippo Mannatzu, Michelangelo Pronko, Andrei G. Mathematical Physics Statistical Mechanics Probability We consider the five-vertex model on a rectangular domain of the square lattice, with the so-called `scalar-product' boundary conditions. We address the evaluation of the free-energy density of the model in the scaling limit, that is when the number of sites is sent to infinity and the mesh of the lattice to zero, while keeping the size of the domain constant. To this aim, we reformulate the partition function of the model in terms of a discrete log-gas, and study its behaviour in the thermodynamic limit. We reproduce previous results, obtained by using a differential equation approach. Moreover, we provide the explicit form of the resolvent in all possible regimes. This work is preliminary to further studies of limit shape phenomena in the model. |
| title | The five-vertex model as a discrete log-gas |
| topic | Mathematical Physics Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2512.23223 |