  We study the motion of phase interfaces in a diffusive lattice equation with
bistable nonlinearity and derive a free boundary problem with hysteresis to
describe the macroscopic evolution in the parabolic scaling limit.
  The first part of the paper deals with general bistable nonlinearities and is
restricted to numerical experiments and heuristic arguments. We discuss the
formation of macroscopic data and present numerical evidence for pinning,
depinning, and annihilation of interfaces. Afterwards we identify a generalized
Stefan condition along with a hysteretic flow rule that characterize the
dynamics of both standing and moving interfaces.
  In the second part, we rigorously justify the limit dynamics for
single-interface data and a special piecewise affine nonlinearity. We prove
persistence of such data, derive upper bounds for the macroscopic interface
speed, and show that the macroscopic limit can indeed be described by the free
boundary problem. The fundamental ingredient to our proofs is a representation
formula that links the solutions of the nonlinear lattice to the discrete heat
kernel and enables us to derive macroscopic compactness results in the space of
continuous functions.
