Journal of Statistical Physics

, Volume 23, Issue 1, pp 49–82 | Cite as

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

  • Giorgio Parisi


We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standardε-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.

Key words

Field theory second-order transitions critical exponents ε-expansion loop expansion renormalization group Callan-Symanzik equation 


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Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Giorgio Parisi
    • 1
  1. 1.Laboratori Nazionali INFNFrascatiItaly

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