  We consider the Ising model with inverse temperature beta and without
external field on sequences of graphs G_n which converge locally to the
k-regular tree. We show that for such graphs the Ising measure locally weak
converges to the symmetric mixture of the Ising model with + boundary
conditions and the - boundary conditions on the k-regular tree with inverse
temperature \beta. In the case where the graphs G_n are expanders we derive a
more detailed understanding by showing convergence of the Ising measure
condition on positive magnetization (sum of spins) to the + measure on the
tree.
