Random transverse and longitudinal field Ising chains

Abstract

Motivated by experimental results on compounds like ${\mathrm{LiHo}}_x{\mathrm{Y}}_{1-x}{\mathrm{F}}_4$, 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 renormalization group (SDRG) 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 behavior 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 one of the two disordered fixed-points and the relevant scaling direction at the infinite disorder fixed-point is along the separatrix, where the correlation-length is shown to diverge with an exponent $\hat{I}{½}_h\approx 1$.

13 pages, 14 figures. arXiv admin note: text overlap with arXiv:2210.09380