  We adapted the SWAP molecular dynamics algorithm for use in lattice Ising
spin models. We dressed the spins with a randomly distributed length and we
alternated long-range spin exchanges with conventional single spin flip Monte
Carlo updates, both accepted with a stochastic rule which respects detailed
balance. We show that this algorithm, when applied to the bidimensional
Edwards-Anderson model, speeds up significantly the relaxation at low
temperatures and manages to find ground states with high efficiency and little
computational cost. The exploration of spin models should help in understanding
why SWAP accelerates the evolution of particle systems and shed light on
relations between dynamics and free-energy landscapes.
