Letters in Mathematical Physics

, Volume 37, Issue 2, pp 137–143

On the extremality of the disordered state for the Ising model on the Bethe lattice

  • Dmitry Ioffe

DOI: 10.1007/BF00416016

Cite this article as:
Ioffe, D. Letters in Mathematical Physics (1996) 37: 137. doi:10.1007/BF00416016


We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k≥2 is extremal if and only if β is less or equal to the spin glass transition value, given by tanh(βcSG= 1/√k.

Mathematics Subject Classifications (1991)

82B20 82B26 82B43 

Key words

Bethe lattice FK representation Ising model 

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Dmitry Ioffe
    • 1
    • 2
  1. 1.Department of MathematicsNorthwestern UniversityU.S.A.
  2. 2.WIASBerlinGermany

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