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We introduce new fast canonical local algorithms for discrete and continuousspin systems. We show that for a broad selection of spin systems they comparefavorably to the known ones except for the Ising +/-1 spins. The new proceduresuse discretization scheme and the necessary information have to be stored incomputer memory before the simulation. The models for testing discrete spinsare the Ising +/-1, the general Ising S or Blume-Capel model, the Potts and theclock models. The continuous spins we examine are the O(N) models, includingthe continuous Ising model (N=1), the \phi^4 Ising model (N=1), the XY model(N=2), the Heisenberg model (N=3), the \phi^4 Heisenberg model (N=3), the O(4)model with applications to the SU(2) lattice gauge theory, and the general O(N)vector spins with N\ge5.Comment: 42 pages, 17 figures, to be pubhlished in Eur. Phys. J.

Canonical local algorithms for spin systems: heat bath and Hasting?s methods