KnowraMean-field theoryLinked fromLinked fromThe 19 pages that link to Mean-field theory, each with the reason it gives.All 19Broader topic 1Related 6Narrower topic 2Compared with 10Universality classCompared with: It often predicts exponents that differ from the true class below the upper critical dimension.Critical phenomenaCompared with: It predicts simple critical exponents but often misses fluctuations in low dimensions.Debye–Hückel theoryNarrower topic: The ionic atmosphere is treated through an averaged electrostatic potential rather than exact ion configurations.Ginzburg–Landau theoryNarrower topic: Standard Ginzburg–Landau treatments use mean-field reasoning near the transition.Coarse-grainingRelated: It is a specific approximation that suppresses fluctuations, rather than a general scale-reduction procedure.Curie–Weiss law (magnetism)Related: It explains how collective interactions produce the law’s temperature offset.Lattice modelCompared with: It suppresses spatial correlations that explicit lattice models can retain.Cavity methodCompared with: Mean-field theory neglects detailed local neighborhoods that cavity methods retain.Vlasov equationRelated: Self-consistent Vlasov fields embody a mean-field treatment of particle interactions.0-dimensional systemsRelated: Mean-field models can suppress spatial correlations, though they need not be genuinely 0-dimensional.1-dimensional systems (physics)Compared with: Its neglect of strong fluctuations often makes it unreliable for one-dimensional systems.Classical spin modelsCompared with: It simplifies spin models but neglects many spatial correlations and fluctuations.Collective behavior in networksCompared with: It suppresses specific network connections that can determine collective outcomes.Collective effects in atomic physicsCompared with: It captures some shared-field behavior but can miss correlations between individual atoms.Disordered systemsCompared with: Averaging can miss spatial fluctuations and rare regions central to disordered systems.Homogeneous networkRelated: Homogeneous networks often enable simpler mean-field approximations of network dynamics.Many-body techniquesCompared with: It is simpler than methods retaining fluctuations and correlations beyond the average field.Mean-field and cluster methodsBroader topic: The single-site limit captures the effective-field strategy shared by these methods.Vlasov–Fokker–Planck modelRelated: The Vlasov part represents collective interactions through an averaged self-consistent field.
KnowraMean-field theoryLinked fromLinked fromThe 19 pages that link to Mean-field theory, each with the reason it gives.All 19Broader topic 1Related 6Narrower topic 2Compared with 10Universality classCompared with: It often predicts exponents that differ from the true class below the upper critical dimension.Critical phenomenaCompared with: It predicts simple critical exponents but often misses fluctuations in low dimensions.Debye–Hückel theoryNarrower topic: The ionic atmosphere is treated through an averaged electrostatic potential rather than exact ion configurations.Ginzburg–Landau theoryNarrower topic: Standard Ginzburg–Landau treatments use mean-field reasoning near the transition.Coarse-grainingRelated: It is a specific approximation that suppresses fluctuations, rather than a general scale-reduction procedure.Curie–Weiss law (magnetism)Related: It explains how collective interactions produce the law’s temperature offset.Lattice modelCompared with: It suppresses spatial correlations that explicit lattice models can retain.Cavity methodCompared with: Mean-field theory neglects detailed local neighborhoods that cavity methods retain.Vlasov equationRelated: Self-consistent Vlasov fields embody a mean-field treatment of particle interactions.0-dimensional systemsRelated: Mean-field models can suppress spatial correlations, though they need not be genuinely 0-dimensional.1-dimensional systems (physics)Compared with: Its neglect of strong fluctuations often makes it unreliable for one-dimensional systems.Classical spin modelsCompared with: It simplifies spin models but neglects many spatial correlations and fluctuations.Collective behavior in networksCompared with: It suppresses specific network connections that can determine collective outcomes.Collective effects in atomic physicsCompared with: It captures some shared-field behavior but can miss correlations between individual atoms.Disordered systemsCompared with: Averaging can miss spatial fluctuations and rare regions central to disordered systems.Homogeneous networkRelated: Homogeneous networks often enable simpler mean-field approximations of network dynamics.Many-body techniquesCompared with: It is simpler than methods retaining fluctuations and correlations beyond the average field.Mean-field and cluster methodsBroader topic: The single-site limit captures the effective-field strategy shared by these methods.Vlasov–Fokker–Planck modelRelated: The Vlasov part represents collective interactions through an averaged self-consistent field.