Dynamics of the Ising Spin-Glass Model in a Transverse Field

TL;DR

This paper investigates the quantum dynamics of the Ising spin-glass model in a transverse field using Monte Carlo and analytic methods, revealing an equivalence to the Kondo model and aligning with experimental data.

Contribution

It establishes an exact equivalence between the spin-glass in a transverse field and the single-impurity Kondo model at criticality, providing new insights into quantum critical behavior.

Findings

Frequency-dependent susceptibility behavior analyzed

Exact equivalence with Kondo model established

Predictions match experimental results on LiHoYF4

Abstract

We use quantum Monte Carlo methods and various analytic approximations to solve the Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above and below the critical field . We establish the existence of an exact equivalence between this problem and the single-impurity Kondo model at the quantum critical point. Our predictions for the long-time dynamics of the model are in good agreement with experimental results on $LiHo_{0.167}Y_{0.833}F_4$.