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Ising model and its relatives are popular in statistical physics. Are there any physical systems that can be characterized by exponential family Markov random fields (e.g., the one in http://arxiv.org/abs/1301.4183), which is a natural generalization of Ising model?

Please explain what exponential family Markov random fields are? I know what exponential families are and what Markov random fields are but never saw the combination - though it sounds interesting. Is it related to http://arxiv.org/abs/1207.4131 by Altun et al. or http://www.jstor.org/stable/2242170 by Comets?

@Arnold Neumaier, I am thinking about the one in this paper http://arxiv.org/abs/1301.4183

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