Abstract
A derivation is given of the magnetic ground states for the spin- 1 2 Ising model with pure four spin interaction on cubic lattices with infinite order parameter dimensionality. The results depend on the periodic boundary conditions that must be used in infinite systems. A new type of boundary condition is thus suggested which enables us to calculate the order parameter dimensionality, with no further assumptions. This system is simpler and gives lower values than those found previously.
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