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A renormalization-group analysis of the spin-1/2 transverse field Ising model with quenched randomness is presented; it become exact asymptotically near the zero temperature ferromagnetic phase transition. The spontaneous magnetization is found to vanish with an exponent =1/2 (3- 5), while in the disordered phase the typical and average spin correlations are found to decay with different correlation lengths, which diverge with exponents \~=1 and =2, respectively.
Daniel S. Fisher (Mon,) studied this question.