Limit Shapes for the Asymmetric Five Vertex Model
Abstract
We compute the free energy and surface tension function for the five-vertex model, a model of non-intersecting monotone lattice paths on the grid in which each corner gets a weight r>0. We give a variational principle for limit shapes in this setting, and show that the resulting Euler-Lagrange equation can be integrated, giving limit shapes explicitly parameterized by analytic functions.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- July 2021
- DOI:
- 10.1007/s00220-021-04126-7
- arXiv:
- arXiv:1812.11934
- Bibcode:
- 2021CMaPh.385..793D
- Keywords:
-
- Mathematics - Probability;
- 82B20
- E-Print:
- 37 pages, 21 figures