Numerical study of the 6-vertex model with domain wall boundary conditions

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A Markov process is constructed to numerically study the phase separation in the 6-vertex model with domain wall boundary conditions. It is a random walk on the graph where vertices are states and edges are elementary moves. It converges to the Gibbs measure of the 6-vertex model. Our results show clearly that a droplet of "c" vertices is created when Boltzamnn weights are in the antisegnetoelectric region. The droplet is a diamond-like shaped curve with four cusps.