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- Critical_dimension abstract "In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory become the same as that in mean field theory. An elegant criterion to obtain the critical dimension within mean field theory is due to V. Ginzburg.Since the renormalization group sets up a relation between a phase transition and a quantum field theory, this has implications for the latter and for our larger understandign of renormalization in general. Above the upper critical dimension, the quantum field theory which belongs to the model of the phase transition is a free field theory. Below the lower critical dimension, there is no field theory corresponding to the model.In the context of string theory the meaning is more restricted: the critical dimension is the dimension at which string theory is consistent assuming a constant dilaton background without additional confounding permutations from background radiation effects. The precise number may be determined by the required cancellation of conformal anomaly on the worldsheet; it is 26 for the bosonic string theory and 10 for superstring theory.".
- Critical_dimension thumbnail CriticalHyperplane.png?width=300.
- Critical_dimension wikiPageExternalLink Kanon_program_83832.html.
- Critical_dimension wikiPageID "1931707".
- Critical_dimension wikiPageLength "10163".
- Critical_dimension wikiPageOutDegree "45".
- Critical_dimension wikiPageRevisionID "688895756".
- Critical_dimension wikiPageWikiLink Bosonic_string_theory.
- Critical_dimension wikiPageWikiLink Category:Critical_phenomena.
- Critical_dimension wikiPageWikiLink Category:Phase_transitions.
- Critical_dimension wikiPageWikiLink Category:Statistical_mechanics.
- Critical_dimension wikiPageWikiLink Category:String_theory.
- Critical_dimension wikiPageWikiLink Conformal_anomaly.
- Critical_dimension wikiPageWikiLink Critical_exponent.
- Critical_dimension wikiPageWikiLink Cutoff_(physics).
- Critical_dimension wikiPageWikiLink Dilaton.
- Critical_dimension wikiPageWikiLink Dimension.
- Critical_dimension wikiPageWikiLink Domain_wall_(string_theory).
- Critical_dimension wikiPageWikiLink Entropy.
- Critical_dimension wikiPageWikiLink Entropy_(statistical_thermodynamics).
- Critical_dimension wikiPageWikiLink Free_field.
- Critical_dimension wikiPageWikiLink Lagrangian_(field_theory).
- Critical_dimension wikiPageWikiLink Linear_algebra.
- Critical_dimension wikiPageWikiLink Mean_field_theory.
- Critical_dimension wikiPageWikiLink Mermin–Wagner_theorem.
- Critical_dimension wikiPageWikiLink Monomial.
- Critical_dimension wikiPageWikiLink Multicritical_point.
- Critical_dimension wikiPageWikiLink Order_and_disorder_(physics).
- Critical_dimension wikiPageWikiLink Path_integral_formulation.
- Critical_dimension wikiPageWikiLink Phase_transition.
- Critical_dimension wikiPageWikiLink Physics.
- Critical_dimension wikiPageWikiLink Quantum_field_theory.
- Critical_dimension wikiPageWikiLink Reciprocal_length.
- Critical_dimension wikiPageWikiLink Renormalization_group.
- Critical_dimension wikiPageWikiLink Scale_invariance.
- Critical_dimension wikiPageWikiLink Schwinger–Dyson_equation.
- Critical_dimension wikiPageWikiLink Statistical_field_theory.
- Critical_dimension wikiPageWikiLink Statistical_mechanics.
- Critical_dimension wikiPageWikiLink String_theory.
- Critical_dimension wikiPageWikiLink Superstring_theory.
- Critical_dimension wikiPageWikiLink Universality_class.
- Critical_dimension wikiPageWikiLink Vertex_function.
- Critical_dimension wikiPageWikiLink Vitaly_Ginzburg.
- Critical_dimension wikiPageWikiLink Worldsheet.
- Critical_dimension wikiPageWikiLink File:CriticalHyperplane.png.
- Critical_dimension wikiPageWikiLinkText "Critical dimension".
- Critical_dimension wikiPageWikiLinkText "critical dimension".
- Critical_dimension wikiPageWikiLinkText "upper critical dimension".
- Critical_dimension wikiPageUsesTemplate Template:For.
- Critical_dimension wikiPageUsesTemplate Template:Refimprove.
- Critical_dimension wikiPageUsesTemplate Template:Reflist.
- Critical_dimension wikiPageUsesTemplate Template:Use_dmy_dates.
- Critical_dimension subject Category:Critical_phenomena.
- Critical_dimension subject Category:Phase_transitions.
- Critical_dimension subject Category:Statistical_mechanics.
- Critical_dimension subject Category:String_theory.
- Critical_dimension hypernym Dimensionality.
- Critical_dimension type Mechanic.
- Critical_dimension type Physic.
- Critical_dimension type Process.
- Critical_dimension type Redirect.
- Critical_dimension type Transition.
- Critical_dimension comment "In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory become the same as that in mean field theory. An elegant criterion to obtain the critical dimension within mean field theory is due to V.".
- Critical_dimension label "Critical dimension".
- Critical_dimension sameAs Q3028070.
- Critical_dimension sameAs Dimension_critique.
- Critical_dimension sameAs m.067116.
- Critical_dimension sameAs Q3028070.
- Critical_dimension wasDerivedFrom Critical_dimension?oldid=688895756.
- Critical_dimension depiction CriticalHyperplane.png.
- Critical_dimension isPrimaryTopicOf Critical_dimension.