Extremality of the disordered state for the Ising model on general trees

Dmitry Ioffe
We develop a method to study extremality of the disordered state ℙ<sup>β</sup> for the Ising model on a general countable tree T. It is shown that the tail σ-field is ℙ<sup>β</sup>-trivial as soon as β is less than the spin glass critical inverse temperature β<sup>S G</sup><sub>c</sub> , which is determined from the relation tanh(β<sup>S G</sup><sub>c</sub>) = 1/√br(T). The method is based on the FK representation of ferromagnetic systems and recursive estimates on conditional expectations of...
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