THE FIVE-VERTEX MODEL AND BOXED PLANE PARTITIONS

摘要

Boxed plane partitions are considered in terms of the five-vertex model on a finite lattice with fixed boundary conditions. Assuming that all weights of the model have the same value, the one-point correlation function describing the probability of having a given state on an arbitrary horizontal edge of the lattice is calculated. This is equivalent to the enumeration of boxed plane partitions that correspond to rhombus tilings of a hexagon with one fixed rhombus of a particular type. The solution of the problem is given for the case of a box of generic size.