  We propose a new Monte Carlo method for efficiently sampling trajectories
with fixed initial and final conditions in a system with discrete degrees of
freedom. The method can be applied to any stochastic process with local
interactions, including systems that are out of equilibrium. We combine the
proposed path-sampling algorithm with thermodynamic integration to calculate
transition rates. We demonstrate our method on the well studied 2D Ising model
with periodic boundary conditions, and show agreement with other results both
for large and small system sizes. The method scales well with the system size,
allowing one to simulate systems with many degrees of freedom, and providing
complementary information with respect to other algorithms.
