, Volume 37, Issue 2, pp 137-143

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

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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(β c SG = 1/√k.