Disorder-Induced Rounding of Certain Quantum Phase Transitions

We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double-exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model system.

Figure 1

Magnetization and susceptibility ($L=100,c=0.2$).

Figure 2

Magnetization and susceptibility close to the seeming transition for different system sizes.

Figure 3

$\log (m)$ as a function of distance from the clean critical point. The solid line is a fit of the average magnetization to Eq. (1b) with $\varphi =2$. The logarithmically averaged data show the onset of the sample-to-sample fluctuations.