WIAS Preprint No. 164, (1995)

A note on the extremality of the disordered state for the Ising model on the Bethe lattice


  • Ioffe, Dmitry


  • Bethe lattice, FK representation, Ising model


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(βSGc) = 1/√k.

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