WeierstraB-Institut fiir Angewandte Analysis und Stochastik Extremality of the disordered state ·for the Ising model on general trees

Im Forschungsverbund, Berlin, Dmitry Ioffe
We develop a method to study extremality of the disordered state JP.B for the Ising model on a general countable tree T. It is shown that the tail CT-field is JP.B-trivial as soon as f3 is less than the spin glass critical inverse temperature f3;a, which is determined from the relation tanh(f3;a) = 1/ Jbr(T). The method is based on the FK representation of ferromagnetic systems and recursive estimates on conditional expectations of the spin at the root. Similar estimates in the context of the
more » ... he context of the bit reconstruction problem on general trees were originally obtained in (EKPS] using different methods.