Upon turning on weak interactions J i n t ≠ ≠ 0 , the Anderson insulator remains many-body localized and order persists deep in the PM/SG phases. Strong enough interactions destroy MBL and the system transitions to a thermalizing phase. The fate of the MBL PM to MBL SG transition in the presence of interactions is presently unsettled, and it is likely this transition proceeds via an intervening thermal phase (Fig 1c).