Expansions for ground state in the transverse field Edwards-Anderson model

It is proven that the ground state in the transverse field Edwards-Anderson model is unique for a sufficiently weak transverse field in a $d$-dimensional finite cubic lattice. On the basis of a recently obtained result for the low energy states in the Edwards-Anderson model, the Kirkwood-Thomas expansion method developed by Datta-Kennedy enables us to show that the uniqueness of ground state is preserved against a sufficiently small transverse field in the transverse field Edwards-Anderson model.