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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| replica symmetry breaking canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6097187 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: replica symmetry breaking Context triple: [Giorgio Parisi, notableWork, replica symmetry breaking]
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A.
Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
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B.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
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C.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
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D.
Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
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E.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: replica symmetry breaking Target entity description: 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.
-
A.
Ising models
Ising models are mathematical models in statistical mechanics that describe systems of interacting binary variables (spins) on a lattice, widely used to study phase transitions, magnetism, and as a foundation for various probabilistic and machine learning models.
-
B.
Yang–Lee theory
Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
-
C.
Lectures on Phase Transitions and the Renormalization Group
*Lectures on Phase Transitions and the Renormalization Group* is a widely used advanced physics textbook that provides a clear, modern introduction to critical phenomena, scaling, and renormalization group methods in statistical mechanics and condensed matter physics.
-
D.
Potts model
The Potts model is a generalization of the Ising model in statistical mechanics that describes interacting spins with more than two possible states, used to study phase transitions and critical phenomena.
-
E.
Boltzmann–Gibbs entropy in statistical mechanics
Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: replica symmetry breaking Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.