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

TL;DR

This paper investigates the critical behavior of Dyson hierarchical quantum ferromagnetic Ising chains with long-range interactions and both pure and random transverse fields using real-space renormalization, deriving critical exponents and comparing with existing methods.

Contribution

It provides explicit critical exponents for the pure case and numerical analysis of the random case, enhancing understanding of long-range quantum ferromagnetic chains.

Findings

Explicit critical exponents as a function of $\sigma$ for pure case

Numerical critical behavior for random case

Comparison with previous renormalization results

Abstract

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