Griffiths Singularities in the Disordered Phase of a Quantum Ising Spin Glass

TL;DR

This study uses Monte Carlo simulations to analyze Griffiths singularities in a disordered quantum Ising spin glass, revealing power law distributions and diverging susceptibilities near the quantum critical point.

Contribution

It provides new insights into the behavior of local susceptibilities and dynamical exponents in a disordered quantum Ising spin glass near criticality.

Findings

Power law distributions of local susceptibility and non-linear susceptibility.

Divergence of local non-linear susceptibility near the quantum transition.

Dynamical exponent z varies smoothly and matches its critical value at the transition.

Abstract

We study a model for a quantum Ising spin glass in two space dimensions by Monte Carlo simulations. In the disordered phase at $T=0$, we find power law distributions of the local susceptibility and local non-linear susceptibility, which are characterized by a smoothly varying dynamical exponent $z$. Over a range of the disordered phase near the quantum transition, the local non-linear susceptibility diverges. The local susceptibility does not diverge in the disordered phase but does diverge at the critical point. Approaching the critical point from the disordered phase, the limiting value of $z$ seems to equal its value precisely at criticality, even though the physics of these two cases seems rather different.