Nonexistence of spontaneous magnetization in Ising models with multiple-spin interactions at high temperatures

A proof is presented to show that there exists no spontaneous magnetization at high temperatures for the Ising model on the square lattice when the interactions are between nearest-neighbour pairs as well as between quartets on the basic plaquettes. The proof can be extended to the general Ising model where the interactions are short-ranged and only between even numbers of spins, and also to the Ising models for which there exist interactions between an odd number of spins, if the Hamiltonian is such that for no product of its terms the power of the spin variable is odd for only one site, when the terms of the external field are discarded.