Applications of exponential family Markov random fields in statistical physics

Question

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?

Comments

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?

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