Six-Vertex Model as a Grassmann Integral, One-Point Function, and the Arctic Ellipse

We formulate the six-vertex model with domain wall boundary conditions in terms of an integral over Grassmann variables. Relying on this formulation, we propose a method calculation correlation functions for case weights satisfying free-fermion condition. consider here details one-point function describing probability given state arbitrary edge lattice. show that thermodynamic limit performed such way lattice is scaled to square unit side length, exhibits “arctic ellipse” phenomenon, agreement previous studies random domino tilings Aztec diamonds: it approaches its limiting values outside ellipse inscribed into square, and takes continuously intermediate inside ellipse. derive also scaling properties vicinity point arctic vicinities points where touches boundary.