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.
Highlights
The six vertex model is a well-known and studied model in statistical mechanics
We briefly review the imaginary time formalism discussed in [19] to the six vertex model with Domain Wall Boundary Conditions (DWBC)
Since fermionic trajectories cannot cross, they are in one-to-one correspondence with a particular edge configuration of the six vertex model
Summary
The six vertex model is a well-known and studied model in statistical mechanics. It was proposed long ago by Linus Pauling [1] to model the ice-water transition and has become an important example of the crucial role that boundary conditions may play in systems that satisfy local constraints such as the ice-rule. In this paper we reconsider the Allison-Reshetikhin algorithm as a tool to obtain numerical estimates of the density profile in the disordered and antiferromagnetic regimes, where essentially no exact results are known. In particular we present an exact finite size expression for the density on the horizontal edges at the free fermion point that shows excellent agreement with the numerics. This is an original and strong test of the reliability of the numerical method that suggests the possibility of its use to obtain accurate quantitative results and qualitative information on the phase diagram. The numerical resolution is not good enough to make a quantitative study in this case
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