Four-vertex Model and Random Tilings

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.

References in corpus (7)

• Thermodynamic limit of the Six-Vertex Model with Domain Wall Boundary Conditions
• Boundary correlation functions of the six-vertex model
• Domino tilings and the six-vertex model at its free fermion point
• Directed-loop Monte Carlo simulations of vertex models
• Boxed Plane Partitions as an Exactly Solvable Boson Model
• Square ice, alternating sign matrices and classical orthogonal polynomials
• Boxed Skew Plane Partition and Integrable Phase Model

Cited by in corpus (6)

• Vertex models, TASEP and Grothendieck polynomials
• The Ising Limit of the XXZ Heisenberg Magnet and Certain Thermal Correlation Functions
• Arctic curves of the four-vertex model
• Determinant formulas for the five-vertex model
• The partition function of the four-vertex model in inhomogeneous external field and trace statistics
• Thermodynamics of the five-vertex model with scalar-product boundary conditions