Canonical local algorithms for spin systems: Heat Bath and Hasting's methods

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising +/-1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising +/-1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the 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.