Away from Criticality: Some Results from the S Matrix Approach

  • Giuseppe Mussardo
Part of the NATO ASI Series book series (NSSB, volume 245)


In two dimensions, conformai invariance provides a natural way to classify the universality classes for critical phenomena [1]. It is of growing interest to extend the Conformai Field Theories (CFT) away from criticality to reach a complete understanding of the scaling region around the fixed points. Zamolodchikov [2] found that particular deformations of the CFT preserve the integrability of the models and the corresponding massive field theories can be described by a factorizable S-matrix. The 5-matrix of the three-state Potts model [3] and the S-matrix of the Ising model in a magnetic field [2] are the first examples of this approach. The hidden E 8 symmetry of Ising model is responsible for the rich structure of the S-matrix in the latter case. Recently, other models have been discussed: the 5-matrix of non-unitary Yang-Lee edge singularity [4] and the S-matrix of the thermal perturbation of the tricritical Ising model [5]. P. Christe will discuss the latter model, expecially its hidden E 7 symmetry, in his talk [6].


Ising Model Dynkin Diagram Conformal Field Theory Thermal Perturbation Coxeter Number 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Giuseppe Mussardo
    • 1
    • 2
  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Sez. di TriesteItaly

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