Thermodynamic Limit of the Free Energy and Correlation Functions of Spin Systems

  • Joel L. Lebowitz
Part of the Acta Physica Austriaca book series (FEWBODY, volume 16/1976)


We give simple proofs of the existence of the thermodynamic limit of the free energy and of equilibrium states for continuous spin systems with “bounded” boundary conditions. For spin-½ Ising systems we show that the infinite volume limit of a state in which there is a field hb > O on the boundaries is the same as that obtained from + boundary conditions (independent of the magnitude of hb). In an appendix with E. Presutti we present stronger results about the existence and uniqueness of equilibrium states for continuous spin systems.


Thermodynamic Limit Gibbs State Ising System Large Magnetic Field Unique Equilibrium State 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Joel L. Lebowitz
    • 1
  1. 1.Belfer Graduate School of ScienceYeshiva UniversityNew YorkUSA

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