The Two-Dimensional Ising Model

  • Philippe Di Francesco
  • Pierre Mathieu
  • David Sénéchal
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


The two-dimensional Ising model is probably one of the most famous statistical models, and it has been extensively studied in the literature. Our aim in this chapter is to present a detailed study of its continuum limit, in the framework of conformally invariant (free fermionic or bosonic) field theories. After reviewing basic facts on the statistical-mechanical model, we concentrate on its continuum fermionic representation. This framework is particularly suitable for the computation of correlation functions of the energy operator on the plane. For correlations involving the spin operator, it is more convenient to consider a bosonic field theory, made of two independent Ising models. In this bosonic formulation, the spin operator has a simple realization in terms of the free field. To complete the study of correlators, we also present the solution of the continuum Ising model on the torus, and use it as an illustrative example of the general theory of conformal blocks covered in Chaps. 9 and 10.


Partition Function Ising Model Energy Operator Ward Identity Conformal Block 
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Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Philippe Di Francesco
    • 1
  • Pierre Mathieu
    • 2
  • David Sénéchal
    • 3
  1. 1.Commissariat l’Énergie Atomique Centre d’Études de SaclayService de Physique ThéoriqueGif-sur-YvetteFrance
  2. 2.Département de PhysiqueUniversité LavalQuébecCanada
  3. 3.Département de PhysiqueUniversité de SherbrookeSherbrookeCanada

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