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Reaching the ground state of a large 2D classical spin model (e.g. classical Heisenberg model) might be a relatively difficult task while using conventional "flip/reject" Monte Carlo method. The system may be easily trapped in a local minima instead of the global minima, for example, the spin domains might appear while you are trying to get a pure ground state.

As far as know there are some techniques can help solve this issue includes "simulated annealing" and "parallel temperature", I would like to know if there are some other techniques might be helpful?

Secondly, many people use Langevin dynamics as an alternative to Monte Carlo method, but I have not tried it yet, I would like to know if the dynamics method has the same "local minima" issue as well?

Any comments and suggestions will be very welcome.

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Although this is a late answer, I hope it could be helpful to others. I happened to have done some work in both Monte Carlo (simulated annealing) and Langevin dynamics of classical spin models. My experience is that both could give you the correct ground state. But the former could be faster, as you can use non-local cluster algorithms to (partially) overcome the critical slowing down problem.

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