replica symmetry breaking
E569064
Replica symmetry breaking is a theoretical framework in statistical physics and spin glass theory that describes how a system’s many equivalent microscopic states can split into a complex hierarchy of inequivalent states, revealing a rugged energy landscape and complex phase structure.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
concept in spin glass theory
ⓘ
concept in statistical physics ⓘ theoretical framework ⓘ |
| appliesTo |
disordered systems
ⓘ
glassy systems ⓘ spin glasses ⓘ |
| basedOn | replica method ⓘ |
| captures |
breaking of permutation symmetry between replicas
ⓘ
hierarchical clustering of states ⓘ multiplicity of pure states ⓘ |
| contrastsWith | replica symmetry ⓘ |
| describes |
complex phase structure
ⓘ
hierarchical organization of states ⓘ nontrivial structure of configuration space ⓘ rugged energy landscape ⓘ splitting of equivalent microscopic states into inequivalent states ⓘ |
| emergesIn | low-temperature phase of spin glasses ⓘ |
| field |
spin glass theory
ⓘ
statistical physics ⓘ |
| frameworkFor |
analyzing energy landscapes with many minima
ⓘ
understanding complex phases in disordered systems ⓘ |
| hasForm |
full replica symmetry breaking
ⓘ
multi-step replica symmetry breaking ⓘ one-step replica symmetry breaking ⓘ |
| historicallyAssociatedWith | Giorgio Parisi NERFINISHED ⓘ |
| implies |
complex free-energy landscape
ⓘ
many metastable states ⓘ non-ergodicity ⓘ |
| indicates |
absence of single thermodynamic pure state
ⓘ
nontrivial distribution of overlaps ⓘ |
| mathematicallyCharacterizedBy |
order parameter function q(x)
ⓘ
overlap distribution between states ⓘ |
| relatedTo |
Parisi solution
NERFINISHED
ⓘ
Sherrington–Kirkpatrick model NERFINISHED ⓘ complex energy landscapes ⓘ glassy dynamics ⓘ mean-field spin glass models ⓘ ultrametricity of states ⓘ |
| requires | analytic continuation in number of replicas ⓘ |
| usedIn |
constraint satisfaction problems
ⓘ
error-correcting codes ⓘ information theory NERFINISHED ⓘ neural network theory ⓘ optimization problems ⓘ random combinatorial problems ⓘ theory of structural glasses ⓘ |
Referenced by (1)
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