  We present implementations of a fourth-order symplectic integrator on graphic
processing units for three $N$-body models with long-range interactions of
general interest: the Hamiltonian Mean Field, Ring and two-dimensional
self-gravitating models. We discuss the algorithms, speedups and errors using
one and two GPU units. Speedups can be as high as 140 compared to a serial
code, and the overall relative error in the total energy is of the same order
of magnitude as for the CPU code. The number of particles used in the tests
range from 10,000 to 50,000,000 depending on the model.
