MONTE CARLO METHOD FOR SPIN MODELS WITH LONG-RANGE INTERACTIONS

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Abstract
We introduce a Monte Carlo method for the simulation of spin models with ferromagnetic long-range interactions in which the amount of time per spin-flip operation is independent of the system size, in spite of the fact that the interactions between each spin and all other spins are taken into account. We work out two algorithms for the q-state Potts model and discuss the generalization to systems with other interactions and to O (n) models. We illustrate the method with a simulation of the mean-field Ising model, for which we have also analytically calculated the leading finite-size correction to the dimensionless amplitude ratio 2/ at the critical temperature.

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