Self-consistent Gaussian approximation study of classical J1-J2 Heisenberg model in honeycomb and diamond lattices

The classical J1-J2 Heisenberg model on bipartite lattice exhibits "Neel" order. However if the AF interactions between the next nearest neighbor(nnn) are increased with respect to the nearest neighbor(nn), the frustration effect arises. In such situations, new phases such as ordered phases with coplanar or spiral ordering and disordered phases such as spin liquids can arise. In this paper we use the self-consistent Gaussian approximation to study the J1-J2 Heisenberg model in honeycomb and diamond lattices. We find the spin liquid phases such as ring-liquid and pancake-liquid in honeycomb lattice.Also for diamond lattice we show that the degeneracy of ground state can be lifted by thermal fluctuations through the order by disorder mechanism