Theorematic Results for the Heisenberg Model

There are some further theorems concerning the signs of various ground-state expectation values (still for bipartite graphs). First [64] for expectations over an exchange operator for an arbitrary pair of sites 

For infinite systems there is another type of result concerning long-range magnetic order, which is implicated in making a material magnetic in the sense that there be a phase transition at the onset, as well as hysteresis. This Neel-state type of ordering concerns the spin correlation function 

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