  We investigate the interface dynamics of the two-dimensional stochastic Ising
model in an external field under helicoidal boundary conditions. At
sufficiently low temperatures and fields, the dynamics of the interface is
described by an exactly solvable high-spin asymmetric quantum Hamiltonian that
is the infinitesimal generator of the zero range process. Generally, the
critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang
universality class of critical behavior. We remark that a whole family of RSOS
interface models similar to the Ising interface model investigated here can be
described by exactly solvable restricted high-spin quantum XXZ-type
Hamiltonians.
