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Tuning the Acceptance

For the Ising model, there is only one possible change to the state: . More generally (e.g., continuous spin models) we are free to make the change in the variable as large or small as we like.

A small change means is small and so the acceptance (proportion of proposed changes that are accepted) is close to 1. But then we move slowly through configuration space. Large changes usually have large and thus low acceptance, which again means that configuration space is not sampled efficiently.

General practice is to do a tradeoff and tune the size of the change so that the acceptance .

Paul Coddington, Northeast Parallel Architectures Center at Syracuse University,