Six-Vertex Model

The six-vertex model assigns arrows to the edges of the square lattice subject to the ice rule that each vertex has two incoming and two outgoing arrows. The six allowed local configurations receive weights, conventionally grouped into three pairs . An allowed global configuration has weight equal to the product of its vertex weights, and normalization gives a probability measure. At , counting these configurations yields Lieb's square ice constant. A height function on faces can be defined, up to an additive constant, by putting the face on the left of an arrow one unit above the face on its right. The ice rule makes the height increments consistent.