Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory

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 ($\mathrm{XY}$) order parameter subject to eightfold symmetry breaking. The latter has a four-component Hamiltonian with two fourth-order invariants. Renormalization-group analysis using $d=4-\epsilon$ expansion indicates, respectively, $\mathrm{XY}$ criticality and, to order ${\epsilon }^2$, a first-order transition. Two connected networks, one ordered and one disordered, can form in the fully frustrated system.