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Symmetry-breaking fields in frustrated Ising systems on square and cubic lattices: Inclusive and exclusive multiphase lines.

A uniform magnetic field is applied to three frustrated Ising systems on square and cubic lattices, breaking the gauge invariance of combined local spin-bond flips. Ordered phases with degeneracy up to 24, accommodating disorder and partial disorder on up to 16 sublattices, are unambiguously identified using the Monte Carlo mean-field method and an approximate transfer-matrix method. The complete phase diagrams for all three systems are obtained in the field-temperature plane and show fluctuation-induced order in two dimensions (2D) and multicritical phenomena and singular lines of degeneracy in three dimensions