Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

► The dynamics of a 2D Ising interface is mapped into the zero range process. ► The generator of the zero range process is equivalent to a high-spin XXZ model. ► We show that a family of asymmetric XXZ Hamiltonians are exactly solvable. ► A whole class of asymmetric high-spin, restricted models belong to the KPZ class.