Simulation of Potts models with real q and no critical slowing down.

A Monte Carlo algorithm is proposed to simulate the ferromagnetic q-state Potts model for any real q>0. A single update is a random sequence of disordering and deterministic moves, one for each link of the lattice. A disordering move attributes a random value to the link, regardless of the state of the system, while in a deterministic move this value is a state function. The relative frequency of these moves depends on the two parameters q and beta=1/kT. The algorithm is not affected by critical slowing down and the dynamical critical exponent z is exactly vanishing. We simulate in this way a three-dimensional Potts model in the range 2<q<3 for estimating the critical value q(c) where the thermal transition changes from second order to first order, and find q(c)=2.620+/-0.005.

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