Frustrated 3×3 Heisenberg antiferromagnets

The full energy spectrum and the exact thermodynamic results of the antiferromagnetic Heisenberg Hamiltonian of the 3×3 triangular and the frustrated square lattice with periodic boundary conditions and s=1/2 are obtained. To this end the method of hierarchy of algebras is employed. It was found that the ground state of the 3×3 frustrated square lattice is a Resonating Valence Bond (RVB) state. Thermodynamic properties, like the specific heat, magnetic susceptibility, the thermal average of the square of the total Sz and entropy, for these two lattices are presented.