Communications in Mathematical Physics

, Volume 66, Issue 2, pp 181–196 | Cite as

Critical point inequalities and scaling limits

  • Charles M. Newman


A refined and extended version of the Buckingham-Gunton inequality relating various pairs of critical exponents is shown to be valid for a large class of statistical mechanical models. If this inequality is an equality (in the refined sense) and one of the critical exponents has a non-Gaussian value, then any scaling limit must be non-Gaussian. This result clarifies the relationship between the nontriviality or triviality of the scaling limit for ordinary critical points in four dimensions (or tricritical points in three dimensions) and the existence of logarithmic factors in the asymptotics which define the two critical exponents.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Large Class 
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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Charles M. Newman
    • 1
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA

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