Restricted annealing of random Ising models

Previous work has shown that the annealed bond Ising model provides a good approximation to the quenched bond Ising model when all the interactions have the same sign. A restricted form of annealing is developed which leads to even better agreement with the quenched model. By placing more and more restrictions on the annealing, successively better approximations to the quenched model can be developed. One of these schemes leads to an exact solution of the quenched problem on triangular cacti.