Related papers: Rare region effects at classical, quantum, and non…
We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with…
In this paper, we review theoretical and experimental research on rare region effects at quantum phase transitions in disordered itinerant electron systems. After summarizing a few basic concepts about phase transitions in the presence of…
These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase…
The Griffiths region that is due to rare regions and the resulting local moments in disordered itinerant quantum magnets, and its influence on the critical behavior, is considered within the framework of an effective field theory. It is…
We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally…
The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk…
We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We…
We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type,…
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase". It is known that, in one dimension, these rare regions can cause the d.c.…
We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with…
We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the overdamping…
We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton…
We employ scaling arguments and optimal fluctuation theory to establish a general relation between quantum Griffiths singularities and the Harris criterion for quantum phase transitions in disordered systems. If a clean critical point…
We investigate the phase transition in a three-dimensional classical Heisenberg magnet with planar defects, i.e., disorder perfectly correlated in two dimensions. By applying a strong-disorder renormalization group, we show that the…
This article reviews the unconventional effects of random disorder on magnetic quantum phase transitions, focusing on a number of new experimental and theoretical developments during the last three years. On the theory side, we address…
In the present paper, first the mathematical basic properties of the exceptional points are discussed. Then, their role in the description of real physical quantum systems is considered. Most interesting value is the phase rigidity of the…
We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to $10^{10}$ and system sizes up to $8000 \times 8000$ sites. Our…
This dissertation describes the effect of quenched randomness on first order phase transitions in lattice systems, classical and quantum. It is proven that a large class of quantum lattice systems in low dimension (d <= 2 or, with suitable…
We study the influence of quenched disorder on quantum phase transitions in systems with over-damped dynamics. For Ising order parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…