A fully frustrated simple cubic lattice with XY and Heisenberg spins: ground state and phase transition

Abstract

The authors study some ground-state properties and the thermodynamics of the fully frustrated simple cubic lattice with classical XY and Heisenberg spins. Using an algorithm which minimises local energies, we find twelve ground-state periodic spin configurations for the XY case, while the degeneracy is probably infinite for the Heisenberg case. The groundstate energy is found to be equal to - square root 3J for both cases, with the same local-field strength for all spins, making the sublattices thermodynamically equivalent in contrast to the Ising case. Various physical quantities are calculated using a Monte Carlo technique. The results show a second-order phase transition in both the XY and Heisenberg cases. Critical exponents are calculated and a crossover is observed.