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(βcSG= 1/√k.
Mathematics Subject Classifications (1991)82B20 82B26 82B43
Key wordsBethe lattice FK representation Ising model
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