Thomas Vojta 2006 J. Phys. A: Math. Gen. 39 R143 doi:10.1088/0305-4470/39/22/R01
Thomas Vojta
Show affiliationsRare 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.
05.70.Fh Phase transitions: general studies
05.70.Jk Critical point phenomena
64.60.A- Specific approaches applied to studies of phase transitions
64.60.Ht Dynamic critical phenomena
82C26 Dynamic and nonequilibrium phase transitions (general)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
82C28 Dynamic renormalization group methods (See also 81T17)
Issue 22 (2 June 2006)
Received 20 February 2006, in final form 4 April 2006
Published 16 May 2006
Thomas Vojta 2006 J. Phys. A: Math. Gen. 39 R143
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