The density profile of the six vertex model with domain wall boundary conditions

Abstract

We study numerically the density profile in the six-vertex model with domain wall boundary conditions. Using a Monte Carlo algorithm originally proposed by Allison and Reshetikhin we numerically evaluate the inhomogeneous density profiles in the disordered and antiferromagnetic regimes where frozen corners appear. At the free fermion point we present an exact finite-size formula for the density on the horizontal edges that relies on the imaginary time transfer matrix approach. In all cases where exact analytic forms for the density and the arctic curves are known the numerical method shows perfect agreement with them. This also suggests the possibility of its use for accurate quantitative purposes.

13 pages, 7 pictures, Published version

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• Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices
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• Phase separation in the six-vertex model with a variety of boundary conditions
• A numerical study of the F-model with domain-wall boundaries
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• Domain wall fluctuations of the six-vertex model at the ice point
• Slow Mixing of Glauber Dynamics for the Six-Vertex Model in the Ordered Phases
• Factorization in the multirefined tangent method
• Breakdown of the thermodynamic limit in quantum spin and dimer models
• Arctic curves of the $6$V model with partial DWBC and double Aztec rectangles
• Torpid Mixing of Markov Chains for the Six-vertex Model on ${\mathbb{Z}}^2$