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This paper studies Medium Access Control (MAC) protocols for regular wireless networks, where only nearest-neighbor interactions are involved. Each station chooses a state in the current time slot, which determines whether it transmits or not, based on its own state and the states of all its nearest neighbors in the previous time slot. The dynamics of the network follow that of a Markov Chain of Markov Fields, which is shown to converge to a stationary distribution for certain types of interactions. It is found that this type of protocols can achieve the optimal one-hop broadcast throughput in regular wireless networks. In case each station can only distinguish between transmitting and idle neighbors, the interactions of the network can be described using the Ising model in statistical mechanics.
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