Abstract
We develop an effective spin theory to describe magnetic properties of the $\nu=2$ Quantum Hall bilayer systems. In the absence of disorder this theory gives quantitative agreement with the results of microscopic Hartree-Fock calculations, and for finite disorder it predicts the existence of a novel spin Bose glass phase. The Bose glass is characterized by the presence of domains of canted antiferromagnetic phase with zero average antiferromagnetic order and short range mean antiferromagnetic correlations. It has infinite antiferromagnetic transverse susceptibility, finite longitudinal spin susceptibility and specific heat linear in temperature. Transition from the canted antiferromagnet phase to the spin Bose glass phase is characterized by a universal value of the longitudinal spin conductance.
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