Quantum Griffiths Singularities in the Transverse-Field Ising Spin Glass

TL;DR

This study uses Monte Carlo simulations to explore Griffiths singularities in quantum Ising spin glasses under a transverse field, revealing their persistence in higher dimensions and their impact on magnetic susceptibilities.

Contribution

It provides the first detailed numerical analysis of Griffiths singularities in 2D and 3D quantum spin glasses, extending understanding beyond one-dimensional systems.

Findings

In 2D, nonlinear susceptibility diverges well above critical field.

In 3D, Griffiths effects are observable but less pronounced.

Griffiths singularities decrease with increasing dimension.

Abstract

We report a Monte Carlo study of the effects of {\it fluctuations} in the bond distribution of Ising spin glasses in a transverse magnetic field, in the {\it paramagnetic phase} in the $T\to 0$ limit. Rare, strong fluctuations give rise to Griffiths singularities, which can dominate the zero-temperature behavior of these quantum systems, as originally demonstrated by McCoy for one-dimensional ($d=1$) systems. Our simulations are done on a square lattice in $d=2$ and a cubic lattice in $d=3$, for a gaussian distribution of nearest neighbor (only) bonds. In $d=2$, where the {\it linear} susceptibility was found to diverge at the critical transverse field strength $\Gamma_c$ for the order-disorder phase transition at T=0, the average {\it nonlinear} susceptibility $\chi_{nl}$ diverges in the paramagnetic phase for $\Gamma$ well above $\Gamma_c$, as is also demonstrated in the accompanying paper by Rieger and Young. In $d=3$, the linear susceptibility remains finite at $\Gamma_c$, and while Griffiths singularity effects are certainly observable in the paramagnetic phase, the nonlinear susceptibility appears to diverge only rather close to $\Gamma_c$. These results show that Griffiths singularities remain persistent in dimensions above one (where they are known to be strong), though their magnitude decreases monotonically with increasing dimensionality (there being no Griffiths singularities in the limit of infinite dimensionality).