From a consideration of the ground states of the antiferromagnetic Ising model a weighting function is proposed. This function preserves the ground states under the renormalisation group transformation. This form of the lower bound approximation leads to results which are in excellent agreement with the exact values in two dimensions and in fair agreement with the approximate results of the series expansion in three dimensions. The implication of this approach for other real-space approximations is noted.
A variational extension of the Migdal–Kadanoff real space renormalization group method is applied to a recently proposed d-dimensional lattice model describing some aspects of molecular orientation in solids. As expected the method yields the exact fixed point for d=2, given the formal equivalence to the two-dimensional Ising model. For d=3 such equivalence breaks down and an approximate estimate of the fixed point is explicitly recovered and compared to the mean-field prediction. The possible existence of an intermediate symmetric phase is discussed.