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

• DOI: 10.1007/bf00416016
• Publication Date: 2004-11-09T11:35:09Z
• Authors: Dmitry Ioffe
• Keywords: Bethe lattice; Lattice (music); Ising spin

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.