Rare region effects at classical, quantum, and non-equilibrium phase transitions

Abstract

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.

Topical review, 68 pages, 14 figures, final version as published

References in corpus (13)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Disorder-Driven Non-Fermi Liquid Behavior of Correlated Electrons
• Quantum Griffiths effects in itinerant Heisenberg magnets
• Critical behavior and Griffiths effects in the disordered contact process
• Absence of conventional quantum phase transitions in itinerant systems with disorder
• Percolation quantum phase transitions in diluted magnets
• Localization effects and inelastic scattering in disordered heavy electrons
• Phase diagrams and universality classes of random antiferromagnetic spin ladders
• Effective model of the electronic Griffiths phase
• Random Antiferromagnetic SU(N) Spin Chains
• Disorder-induced phases in the S=1 antiferromagnetic Heisenberg chain
• Magnetic droplets in a metal close to a ferromagnetic quantum critical point
• Percolation of satisfiability in finite dimensions

Cited by in corpus (26)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Effects of dissipation on a quantum critical point with disorder
• Infinite-randomness quantum critical points induced by dissipation
• Theory of smeared quantum phase transitions
• Electronic Griffiths phase of the d=2 Mott transition
• Infinite randomness fixed point of the superconductor-metal quantum phase transition
• Weakly disordered absorbing-state phase transitions
• Quantum phase transitions of the diluted O(3) rotor model
• Finite temperature behavior of strongly disordered quantum magnets coupled to a dissipative bath
• Percolation transition and dissipation in quantum Ising magnets
• Quantum Critical Behavior of the Cluster Glass Phase
• On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
• Absorbing-state phase transitions on percolating lattices
• Thermal expansion and Grueneisen parameter in quantum Griffiths phases
• Magnetocaloric Studies of the Peak Effect in Nb
• A theoretical study of the cluster glass-Kondo-magnetic disordered alloys
• Local defect in a magnet with long-range interactions
• Griffiths-McCoy singularities, Lee-Yang zeros and the cavity method in a solvable diluted ferromagnet
• Static and dynamic structure factors in three-dimensional randomly diluted Ising models
• Dissipation effects in percolating quantum Ising magnets
• Renormalization-group investigation of the S=1 random antiferromagnetic Heisenberg Chain
• Slow dynamics at the smeared phase transition of randomly layered magnets
• The contact process in disordered and periodic binary two-dimensional lattices
• Ordered droplets in quantum magnets with long-range interactions