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Limit Shapes for the Asymmetric Five Vertex Model
- Source :
- Communications in Mathematical Physics. 385:793-836
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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 positive weight. We give a variational principle for limit shapes in this setting, and show that the resulting Euler-Lagrange equation can be integrated, giving explicit limit shapes parameterized by analytic functions.<br />37 pages, 21 figures
- Subjects :
- Probability (math.PR)
82B20
010102 general mathematics
Mathematical analysis
Lattice (group)
Parameterized complexity
Statistical and Nonlinear Physics
Function (mathematics)
01 natural sciences
Monotone polygon
Variational principle
0103 physical sciences
Vertex model
FOS: Mathematics
010307 mathematical physics
Limit (mathematics)
0101 mathematics
Mathematics - Probability
Mathematical Physics
Mathematics
Analytic function
Subjects
Details
- ISSN :
- 14320916 and 00103616
- Volume :
- 385
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....b1437ff2b9151f922fc3c83f5e5f6971