Fully frustrated simple cubic lattices and the overblocking effect

Abstract

Fully frustrated simple cubic (sc) lattices are investigated, following the study of face centred cubic lattices by S. Alexander and P. Pincus, in order to determine what are the universal properties of such Ising models. The overblocking effect, compulsory appearance of overfrustrated plaquettes due to geometric hindrances, is shown to take place for sc lattices also, above dimension four. The ground state average internal field is shown to behave similarly in both lattice families. Other features are found to differ : no periodicity in dimension (instead of periodicity two), ground state degeneracy. A scaling procedure allows explicit constructions to be made of ground states up to d = 7 for sc lattices, and in any dimension for fcc lattices. Upper and lower bounds for the ground state energies of sc lattices are given for d ≽ 8. The diamond lattice is also discussed