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The Dyson hierarchical version of the quantum Ising chain with Long-Rangedpower-law ferromagnetic couplings $J(r) \propto r^{-1-\sigma}$ and pure orrandom transverse fields is studied via real-space renormalization. For thepure case, the critical exponents are explicitly obtained as a function of theparameter $\sigma$, and are compared with previous results of other approaches.For the random case, the RG rules are numerically applied and the criticalbehaviors are compared with previous Strong Disorder Renormalization results.

Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields