Existence of spin-glass phases for three- and four-dimensional Ising and Heisenberg models

Using Migdal's recursion relations the authors investigate the existence of spin-glass phases for bond-diluted Ising and Heisenberg models with randomly distributed nearest-neighbour ferro- and antiferromagnetic interactions. For three-dimensional systems a spin-glass phase can only exist at zero temperature, while four-dimensional systems exhibit spin-glass phases at finite temperature. They show that very general considerations imply strong restrictions on the form of 1D recursion relations. As a consequence, the qualitative properties of all the systems they considered are very close.