Random transverse field Ising spin chains.

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 \ensuremath{\beta}=1/2(3- \ensuremath{\surd}5 ), while in the disordered phase the typical and average spin correlations are found to decay with different correlation lengths, which diverge with exponents \ensuremath{\nu}\ifmmode \tilde{}\else \~{}\fi{}=1 and \ensuremath{\nu}=2, respectively.