Journal of Statistical Physics, Vol. 55, Nos. 5/6, 1989. p. 1263-1277.
The effect of collective modes on the otherwise local structure of Ising lattices is investigated by studying a number of exactly solvable models. First, the open one-dimensional Ising model serves to define sharp locality. This feature then remains upon extension to a Bethe lattice, despite the existence of a phase transition. But insertion of periodic boundary conditions creates a collective mode which breaks locality in a very specific fashion. A model interface is analyzed to show that even when locality is not broken, local uniformity can become untenable.