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| Disordered systems | |
|---|---|
| Name | Disordered systems |
| Field | Statistical mechanics; Condensed matter physics |
| Introduced | 20th century |
Disordered systems are materials and models in which structural, compositional, or interaction irregularities break the translational symmetry characteristic of crystalline solids. Such systems include amorphous solids, spin glasses, random alloys, and networked media whose properties are dominated by spatial or energetic randomness rather than periodic order. Study of these systems connects to phenomena observed in condensed matter, materials science, and complex systems, and has influenced research associated with phase behavior, slow dynamics, and emergent collective phenomena.
Disorder appears in many contexts from quenched impurities in Anderson localization to glassy dynamics in Edwards–Anderson model, and is relevant to experiments at facilities like CERN and Oak Ridge National Laboratory where materials with defects are characterized. Foundational contributions trace to figures such as Philip W. Anderson, Leon N. Cooper, and Sir Nevill Mott, and conceptual frameworks were advanced in works associated with the Sherrington–Kirkpatrick model and by researchers at institutions including Bell Labs and Los Alamos National Laboratory. Interdisciplinary links connect disorder research with topics studied by scholars at Massachusetts Institute of Technology, University of Cambridge, and Princeton University.
Disordered systems are classified by the nature and statistics of irregularities: quenched versus annealed disorder; site versus bond randomness; short-range versus long-range correlated disorder. Examples include substitutional disorder in Hume-Rothery rules alloys, structural disorder in materials studied at Max Planck Institute for Solid State Research, topological disorder in networks relevant to Royal Society workshops, and dynamical disorder in systems explored by groups at Caltech and Stanford University. Specific taxa include electronic disorder (treated near themes by Anderson localization), magnetic disorder (explored in experiments at National High Magnetic Field Laboratory), and structural glasses (investigated in research programs at Harvard University).
Core models include the Edwards–Anderson model, Sherrington–Kirkpatrick model, random-field Ising model, percolation models developed in studies related to Alexander Grothendieck-adjacent mathematics, and models of localization due to Philip W. Anderson. Methods employ techniques from replica theory as used by groups led by Giorgio Parisi, renormalization group approaches exemplified in work by Kenneth G. Wilson, supersymmetric methods influenced by researchers at Institute for Advanced Study, and numerical strategies pioneered by teams at Los Alamos National Laboratory and IBM. Mathematical foundations draw on probability theory developed by scholars connected to Andrey Kolmogorov, large deviations frameworks associated with Varadhan, and combinatorial perspectives informed by seminars at Courant Institute.
Experimental probes of disorder include neutron scattering at facilities like Oak Ridge National Laboratory and Institut Laue–Langevin, X-ray diffraction campaigns at European Synchrotron Radiation Facility, transport measurements in setups used by researchers at Bell Labs, and spectroscopies performed at Lawrence Berkeley National Laboratory. Observables include conductivity measured in experiments influenced by Nobel Prize in Physics work on localization, specific heat curves recorded in studies by groups at University of Chicago, magnetic susceptibility measured in experiments referencing techniques from National Institute of Standards and Technology, and aging or memory effects analyzed in laboratory programs at University of Oxford and University of California, Berkeley.
Disordered media exhibit modified phase transitions such as smeared transitions in random-field systems and Griffiths phases first discussed in contexts related to work by Robert B. Griffiths. Critical behavior can be altered by disorder relevance criteria formalized in studies by John Cardy and through renormalization-group flows explored in collaborations with Michael E. Fisher. Spin-glass transitions were elucidated in theoretical developments by Giorgio Parisi and experimental confirmation efforts at institutions including Argonne National Laboratory and ETH Zurich. Concepts such as universality classes, finite-size scaling, and rare-region effects are central to modern analyses pursued at Imperial College London.
Practical examples span amorphous semiconductors used in devices at Intel, disordered superconductors relevant to research at Niels Bohr Institute, porous media important to studies at Shell and BP for reservoir characterization, and biological networks whose heterogeneity is investigated by groups at Sanger Institute. Technological applications include noise-tolerant architectures inspired by spin-glass ideas in work at Google and Microsoft Research, random laser systems explored in laboratories linked to École Normale Supérieure, and optimization algorithms derived from replica and belief-propagation methods applied by teams at Facebook and DeepMind.
Active questions concern many-body localization investigated by collaborations involving Perimeter Institute and Stanford Institute for Theoretical Physics, the nature of the glass transition debated among researchers at Yale University and Princeton University, rigorous characterization of universality in Random Field models pursued by groups at University of Cambridge and Utrecht University, and computational complexity connections illuminated by theorists at Institute for Advanced Study. Emerging directions include topological aspects of disorder studied at Max Planck Institute for the Physics of Complex Systems, machine-learning approaches to disorder modeling developed at Carnegie Mellon University, and quantum simulators addressing disordered Hamiltonians in experiments at MIT and Harvard University.