Coleman theorem on symmetry breaking in two dimensions
E573375
The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Coleman theorem on symmetry breaking in two dimensions canonical | 1 |
| Mermin–Wagner theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6155419 — 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: Coleman theorem on symmetry breaking in two dimensions Context triple: [Sidney Coleman, notableIdea, Coleman theorem on symmetry breaking in two dimensions]
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A.
Kramers–Wannier duality in the Ising model
Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
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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.
-
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.
Landau theory of second-order phase transitions
Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
-
E.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
- 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: Coleman theorem on symmetry breaking in two dimensions Target entity description: The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
-
A.
Kramers–Wannier duality in the Ising model
Kramers–Wannier duality in the Ising model is a mathematical transformation that relates the high-temperature and low-temperature phases of the two-dimensional Ising model, revealing the location of its critical point and illustrating a deep symmetry between ordered and disordered states.
-
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.
Landau theory of second-order phase transitions
Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
-
E.
Luttinger liquid theory
Luttinger liquid theory is a framework describing the collective, non-Fermi-liquid behavior of interacting electrons in one-dimensional conductors, where excitations are best understood as bosonic density waves rather than quasiparticles.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
no-go theorem
ⓘ
theorem in quantum field theory ⓘ |
| appliesTo |
1+1 dimensional relativistic quantum field theories
ⓘ
two-dimensional spacetime ⓘ |
| assumes |
existence of a unique translationally invariant vacuum
ⓘ
locality ⓘ positivity of the Hilbert space metric ⓘ relativistic invariance ⓘ short-range interactions ⓘ |
| clarifies | conditions under which Goldstone’s theorem fails in two dimensions ⓘ |
| concerns |
continuous global symmetries
ⓘ
spontaneous symmetry breaking ⓘ |
| consequence |
no phase with spontaneously broken continuous symmetry exists in 1+1D relativistic QFT under its assumptions
ⓘ
order parameters for continuous symmetries cannot acquire nonzero vacuum expectation values in 1+1D ⓘ |
| doesNotApplyTo |
discrete symmetries
ⓘ
higher-dimensional spacetimes ⓘ |
| excludes | long-range order associated with continuous symmetries in two-dimensional relativistic QFT ⓘ |
| field |
quantum field theory
ⓘ
theoretical physics ⓘ |
| formalism | operator formalism of quantum field theory ⓘ |
| holdsFor |
continuous internal symmetries
ⓘ
global symmetries ⓘ |
| implies |
absence of Goldstone bosons for continuous symmetries in two-dimensional relativistic quantum field theories
ⓘ
vacuum expectation values of local order parameters for continuous symmetries vanish in two dimensions ⓘ |
| influenced | understanding of phase structure in low-dimensional quantum field theories ⓘ |
| involves |
cluster decomposition properties
ⓘ
correlation functions of fields ⓘ infrared behavior of propagators ⓘ |
| mathematicalContext | relativistic quantum fields on two-dimensional Minkowski space ⓘ |
| namedAfter | Sidney Coleman NERFINISHED ⓘ |
| originalAuthor | Sidney Coleman NERFINISHED ⓘ |
| publishedIn | Communications in Mathematical Physics NERFINISHED ⓘ |
| reason | large infrared fluctuations of massless modes in two dimensions ⓘ |
| relatedTo |
Goldstone theorem
NERFINISHED
ⓘ
Mermin–Wagner theorem NERFINISHED ⓘ infrared divergences ⓘ massless scalar fields in two dimensions ⓘ |
| statesThat | continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime ⓘ |
| typeOf | infrared no-go result ⓘ |
| usedIn |
analysis of two-dimensional sigma models
ⓘ
constraining model building in 1+1 dimensional QFT ⓘ study of two-dimensional scalar field theories ⓘ |
| yearProposed | 1973 ⓘ |
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Subject: Coleman theorem on symmetry breaking in two dimensions Description of subject: The Coleman theorem on symmetry breaking in two dimensions is a result in quantum field theory stating that continuous symmetries cannot undergo spontaneous symmetry breaking in two-dimensional spacetime due to large infrared fluctuations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Mermin–Wagner theorem