Fully frustrated simple cubic lattices and phase transitions

Abstract

We give the explicit expression of the free energy for the Gaussian model and the spherical model on a fully frustrated simple cubic lattice in all dimensions, and compare the results with the ferromagnetic case. For the spherical model, the critical temperature is lower by a factor 2 than the temperature predicted by the usual mean field theory, whereas the Bethe approximation does not predict any transition. We also study the high dimension expansion of the free energy, and conclude that this expansion may hide the transitions. These results show that some difficulties encountered in models of spin glasses also appear in models with non-random interactions