Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 167–187 | Cite as

Spontaneous Symmetry Breaking of a Hyperbolic Sigma Model in Three Dimensions

  • T. SpencerEmail author
  • M.R. Zirnbauer


Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H2, the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Electron System 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Institut für Theoretische PhysikUniversität zu KölnGermany

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