Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions

Abstract

The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent nu in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent nu are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.

12 pages, 15 figures, minor revision in version 2

References in corpus (2)

• Renormalization group study of random quantum magnets
• Real-space renormalization group for the transverse-field Ising model in two and three dimensions

Cited by in corpus (22)

• Quantum critical dynamics in a 5000-qubit programmable spin glass
• Quantum Annealing: An Overview
• Strong Disorder RG approach - a short review of recent developments
• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Unconventional critical activated scaling of two-dimensional quantum spin-glasses
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Periodically driven random quantum spin chains : Real-Space Renormalization for Floquet localized phases
• Critical properties of the contact process with quenched dilution
• Pure and Random Quantum Ising Chain : Shannon and Renyi entropies of the ground state via real space renormalization
• Block Renormalization for quantum Ising models in dimension $d=2$ : applications to the pure and random ferromagnet, and to the spin-glass
• Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
• Star junctions and watermelons of pure or random quantum Ising chains : finite-size properties of the energy gap at criticality
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• Random quantum Ising model with three-spin couplings
• Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
• Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet
• Multifractality in aperiodic quantum spin chains
• Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube
• Evidence of de Almeida-Thouless line below six dimensions
• Energy gap of quantum spin glasses: a projection quantum Monte Carlo study