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 {β}=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 {ν} ̃ \~{}{}=1 and {ν}=2, respectively.
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Daniel S. Fisher (1992) studied this question.