Rare Region Effects At Classical, Quantum and Nonequilibrium Phase Transitions
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.
T. Vojta, "Rare Region Effects At Classical, Quantum and Nonequilibrium Phase Transitions," Journal of Physics A: Mathematical and General, Institute of Physics - IOP Publishing, Jun 2006.
The definitive version is available at https://doi.org/10.1088/0305-4470/39/22/R01
National Science Foundation (U.S.)
University of Missouri Research Board
Keywords and Phrases
Griffiths Singularity; Rare Large Spatial Disorder Fluctuations; Rare Regions; Heisenberg uncertainty principle; Ising model; Phase transformations (Statistical physics)
Article - Journal
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