We present a simple algorithm that perfectly samples configurations from the unique Gibbs measure of a spin system on a potentially infinite graph G. The sampling algorithm assumes strong spatial mixing together with subexponential growth of G. It produces a finite window onto a perfect sample from the Gibbs distribution. The run-time is linear in the size of the window, in particular it is constant for each vertex.
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Anand et al. (2022) studied this question.
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