We revisit the physics of electron gas bilayers in the quantum Hall regime [Nature, 432 (2004) 691; Science, 305 (2004) 950], where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation of a BEC of excitons in the half-filled electron bilayers, where empty states play the role of holes. We discuss the fundamental difficulties with this scenario, and propose an alternative approach based on a treatment of the system as a pseudospin magnet. We show that the experimentally observed tunneling peak can be linked to the XY ferromagnet (FM) to Ising antiferromagnet (AFM) phase transition of the S=1/2 XXZ pseudospin model, driven by the change in total electron density. This transition is accompanied by a qualitative change in the nature of the low energy spin wave dispersion from a gapless linear mode in the XY-FM phase to a gapped, quadratic mode in the Ising-AFM phase.
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