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

TL;DR

This study investigates critical and Griffiths-McCoy singularities in quantum Ising spin glasses across various dimensions using series expansions, revealing mean-field agreement in high dimensions and complex singular behavior in lower dimensions.

Contribution

It provides the first detailed analysis of singularities in quantum Ising spin glasses across dimensions, highlighting the dimensional dependence of Griffiths-McCoy effects and critical behavior.

Findings

Mean-field critical properties match exact results in high dimensions.

Strong Griffiths-McCoy singularities occur in low dimensions.

Susceptibilities diverge before the critical point in the paramagnetic phase.

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 $\textit{before}$ 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.