The partition function of the four-vertex model in inhomogeneous external field and trace statistics
Statistical Mechanics
2020-11-23 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal form. The established connection with the boxed plane partitions allows us to calculate the generating function of plane partitions with the fixed sums of their diagonals. The obtained results are another example of the connection of integrable models with the enumerative combinatorics.
Keywords
Cite
@article{arxiv.2011.10200,
title = {The partition function of the four-vertex model in inhomogeneous external field and trace statistics},
author = {Nikolay Bogoliubov and Cyril Malyshev},
journal= {arXiv preprint arXiv:2011.10200},
year = {2020}
}
Comments
18 pages, 6 figures. arXiv admin note: text overlap with arXiv:0711.0030