With both random transverse and longitudinal fields present, RG trajectories flow to disordered fixed points and the correlation-length exponent at the infinite-disorder fixed point along the separatrix is approximately 1.
For the longitudinal field, we assume that it acts only on a fraction of sites, ζ ≤ 1, thus ci = ( 1 with probability ζ , 0 with probability (1 − ζ)
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Random transverse and longitudinal field Ising chains
With both random transverse and longitudinal fields present, RG trajectories flow to disordered fixed points and the correlation-length exponent at the infinite-disorder fixed point along the separatrix is approximately 1.