Medium access control (MAC) protocols where only nearest-neighbor interactions are involved are studied for 1-D and 2-D regular wireless networks. 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 Field, which is shown to converge to a stationary distribution under certain conditions on the interactions. It is found that this type of protocols can achieve the optimal one-hop broadcast throughput in regular 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. Such 1-D networks can be analyzed exactly, whereas for 2-D networks, MAC protocols are designed to achieve near-optimum throughput.