Corner transfer matrix

Summary

A corner transfer matrix is the partition function of one quarter of a square-lattice region. It is viewed as a matrix indexed by the spins on the two edges of the quarter that meet at the centre. Four such matrices, one per quadrant, multiply to give the partition function of the whole region. Inserting a spin at the centre gives one-point functions such as the magnetization. Baxter introduced them in 1968, and for models that satisfy the star–triangle relation they can be diagonalized in the infinite-volume limit. This led to exact formulas for order parameters, for example in the hard hexagon model.