Communications in Mathematical Physics

, Volume 128, Issue 1, pp 63–76 | Cite as

Ising models on the Lobachevsky plane

  • C. M. Series
  • Ya. G. Sinai


We consider the Ising model on a lattice which is the orbit of a discrete cocompact group acting on the hyperbolic plane. For large values of the inverse temperature we construct an uncountable number of mutually singular Gibbs states.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • C. M. Series
    • 1
  • Ya. G. Sinai
    • 2
  1. 1.Mathematics InstituteWarwick UniversityCoventryUK
  2. 2.Landau Institute for Theoretical PhysicsAcademy of Sciences of the USSRMoscowUSSR

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