Ground states and the nature of a phase transition in a simple cubic fully frustrated Ising model

Abstract

The ground state of a fully frustrated simple cubic lattice on $N$ Ising spins is worked out. A degeneracy of the order $2^{\frac{N^{\frac{2}{3}}}{4}}$ is found. A possible phase transition is discussed within a Bethe-Peierls approximation and on the basis of symmetry arguments. The transition temperature is in good agreement with recent computer simulations.