Abstract
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. These singular lines, which occur in two versions as inclusive and exclusive multiphase lines, are distinct from first-order lines of coexistence and constitute a type of phase behavior that is typical for systems possessing a high degree of degeneracy.
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