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 sheds light on relations between dynamics and free-energy landscapes.

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• Nonequilibrium statistical mechanics
• Renormalization group
• Glassy systems
• Cavity methods
• Finite-size scaling
• Ising model
• Metropolis algorithm
• Monte Carlo methods
• Random bond Ising model
• Simulated annealing
• Spin lattice models