Abstract Motivated by experimental results on compounds like LiHo x Y 1 − x F 4 , we consider an Ising chain with random bonds in the simultaneous presence of random transverse and longitudinal fields. We study the low-energy properties of the model at zero temperature by the strong disorder renormalisation group method. In the absence of random longitudinal fields, the model showcases a trivial quantum-ordered and quantum-disordered fixed-point and a non-trivial infinite disorder critical point. In the absence of random transverse fields, the behaviour is dictated by the classical random-field Ising fixed-point. In the simultaneous presence of both a longitudinal and transverse random field, the RG trajectories are attracted to a set of disordered fixed-points, in which the disorder is either due to random quantum fluctuations, or due to classical random-field effects. Between the two regimes there is a smooth cross-over, which becomes sharp at the infinite disorder fixed-point. This local separatrix defines the relevant scaling direction, where the correlation-length is shown to diverge with an exponent ν h ≈ 1 .
Pető et al. (Mon,) studied this question.