Four-vertex Model and Random Tilings

TL;DR

This paper analyzes the exactly solvable four-vertex model on a square grid, using algebraic methods to connect it with plane partitions and tiling models, providing exact solutions and insights into boundary condition effects.

Contribution

It introduces an algebraic Bethe Ansatz approach to compute the partition function and links the model to plane partitions and tilings, expanding understanding of boundary condition impacts.

Findings

Partition function calculated explicitly for fixed boundary conditions

Connection established between scalar products and plane partitions

Discussion of tiling models on periodic grids

Abstract

The exactly solvable four-vertex model on a square grid with the different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model. For the fixed boundary conditions the connection of the scalar product of the state vectors with the generating function of the column and row strict boxed plane partitions is established. Tiling model on a periodic grid is discussed.