The 2D Fully Frustrated XY(FFXY) class of models is shown to contain a new ground-state in addition to the checkerboard groundstate of the standard 2D XY model. The spin configuration of this additional groundstate is obtained and its connection to a broken Z2-symmetry explained. This means that the class of 2D FFXY models belongs within a U(1) × Z_2 × Z_2-symmetry phase-transition representation. The phase diagram is reviewed and the central charges of the four multicritical points described. The im-plications for the standard 2D FFXY-model are discussed and elucidated, in particular with respect to the long standing controversy concerning the phase transitions of the standard 2D FFXY-model.
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