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I would like to simulate a 2D classical spin system, whose interactions are only nearest neighbor, using Monte Carlo. I would like to use Metropolis for updating. I have seen that when updating one can choose a lattice site at random, or update sequentially. I was wondering if it is possible to update part of the lattice simultaneously by considering only a sub-lattice. For instance, let the lattice be $L \times L$ with $L$ even. Indexing from zero, call every site whose sum of their $x$ and $y$ coordinates is odd part of sub-lattice $A$, and every other site sub-lattice $B$. Is it acceptable to compute probabilities of spin acceptances for all of $A$ simultaneously and then implement those spin changes simultaneously? Then subsequently for $B$?

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There is a large amount of literature on the kind of moves and updates you can do in MCMC methods for spin systems. I would start by reading some of the recent papers of Helmut Katzgraber and the references he has.

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  • $\begingroup$ I'll be sure to check them out, but could you provide an answer in your answer, like "yes because..." or "no because..." If you don't know, maybe this should just be a comment, not an answer... $\endgroup$ – kηives Feb 1 '15 at 19:26
  • $\begingroup$ Well, the answer is complicated. You can come up with many ways to define moves in MCMC schemes. Almost all of them are valid in some way or other in that they make the scheme converge if you allow sufficiently many iterations. The question simply is whether they make the scheme converge faster than the trivial single-spin-flip move. And that is often a matter of experimentation, rather than theory, so it doesn't have a clear yes/no answer. $\endgroup$ – Wolfgang Bangerth Feb 1 '15 at 22:09

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