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Ising models are studied, with frustration covering either only the x-y planes, or all the planes of a simple-cubic lattice. The former reveals a two-component (XY) order parameter subject to eightfold symmetry breaking. The latter has a four-component Hamiltonian with two fourth-order invariants. Renormalization-group analysis using d=4-ε expansion indicates, respectively, XY criticality and, to order ε², a first-order transition. Two connected networks, one ordered and one disordered, can form in the fully frustrated system.
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Blankschtein et al. (1984) studied this question.
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