  We construct a lattice field theory method for computing the real-time
dynamics of spin systems in a thermal bath. This is done by building on
previous work of Takano with Schwinger-Keldysh and functional differentiation
techniques. We derive a Schwinger-Keldysh path integral for generic spin
Hamiltonians, then demonstrate the method on a simple system. Our path integral
has a sign problem, which generally requires exponential run time in the system
size, but requires only linear storage. The latter may place this method at an
advantage over exact diagonalization, which is exponential in both. Our path
integral is amenable to contour deformations, a technique for reducing sign
problems.
