Quantum antiferromagnets with competing interactions

By applying the method of hierarchy of algebras, we derive exact thermodynamic results of the square 4×4 lattice and of the linear ring of 16 spins described by an isotropic Heisenberg Hamiltonian. Next-nearest-neighbour interactions are taken into account. The entropy, the specific heat, magnetic susceptibility and the thermal average of the square of the total Sz for various values of the relative strength of the second neighbour interactions are discussed.