Some explicit results for the generalized emptiness formation probability of the six-vertex model (Q2314404)

The six-vertex model on a square lattice is considered with the generalized emptiness formation probability (GEFP). The GEFP is the probability of ferroelectric order around all vertices belonging to a Ferrers diagram \(\lambda\) located at the top left corner of the lattice. The authors consider the GEFP in the case of \(\lambda\) having the shape of a triangle. Various explicit formulas for the GEFP are presented and compared. Under some conditions on parameters of the model, some relations between the GEFP and the Painlevé VI are found.