Ising model states taking on values {0,1} vs {-1,1}.

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I have seen descriptions of the Ising model taking on values {-1,1}, as well as taking on values {0,1}. I understand the {-1,1} representation is the more traditional option, though very reputable sources have presented the model where nodes are restricted to {0,1} (Wainwright, Jordan et al 2008). Both formulations have the same energy function. I am curious if parameter estimation for both would result in equivalent models?