Critical and Griffiths-McCoy singularities in quantum Ising spin-glasses on d-dimensional hypercubic lattices: A series expansion study

Abstract

We study the $\pm J$ transverse-field Ising spin glass model at zero temperature on d-dimensional hypercubic lattices and in the Sherrington-Kirkpatrick (SK) model, by series expansions around the strong field limit. In the SK model and in high-dimensions our calculated critical properties are in excellent agreement with the exact mean-field results, surprisingly even down to dimension $d=6$ which is below the upper critical dimension of $d=8$. In contrast, in lower dimensions we find a rich singular behavior consisting of critical and Griffiths-McCoy singularities. The divergence of the equal-time structure factor allows us to locate the critical coupling where the correlation length diverges, implying the onset of a thermodynamic phase transition. We find that the spin-glass susceptibility as well as various power-moments of the local susceptibility become singular in the paramagnetic phase $\text{before}$ the critical point. Griffiths-McCoy singularities are very strong in two-dimensions but decrease rapidly as the dimension increases. We present evidence that high enough powers of the local susceptibility may become singular at the pure-system critical point.

arXiv comment5 pages, 4 figures. Replaced by new version with an additional figure (Fig. 3) not present in the published version

References in corpus (9)

• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Landau theory of quantum spin glasses of rotors and Ising spins
• Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• A Solvable Spin-Glass of Quantum Rotors
• Quantum Griffiths Singularities in the Transverse-Field Ising Spin Glass
• Quantum Griffiths phase inside the ferromagnetic phase of Ni${}_{1-x}$V${}_x$
• Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion
• Unconventional critical activated scaling of two-dimensional quantum spin-glasses

Cited by in corpus (12)

• Quantum Annealing: An Overview
• Next-Generation Topology of D-Wave Quantum Processors
• The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on the quantum hardware
• Projective cluster-additive transformation for quantum lattice models
• Spin-glass dynamics: experiment, theory and simulation
• Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study
• Dynamic structure factor of Heisenberg bilayer dimer phases in the presence of quenched disorder and frustration
• Efficient generation of series expansions for $\pm J$ Ising spin-glasses in a classical or a quantum (transverse) field
• Energy gap of quantum spin glasses: a projection quantum Monte Carlo study
• Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs