  We have extended the application of quantum renormalisation group (QRG) to
the anisotropic Heisenberg model with next-nearest neighbour (n-n-n)
interaction. The second order correction has to be taken into account to get a
self similar renormalized Hamiltonian in the presence of n-n-n-interaction. We
have obtained the phase diagram of this model which consists of three different
phases, i.e, spin-fluid, dimerised and Ne'el types which merge at the
tri-critical point. The anisotropy of the n-n-n-term changes the phase diagram
significantly. It has a dominant role in the Ne'el-dimer phase boundary. The
staggered magnetisation as an order parameter defines the border between
fluid-Ne'el and Ne'el-dimer phases. The improvement of the second order RG
corrections on the ground state energy of the Heisenberg model is presented.
Moreover, the application of second order QRG on the spin lattice model has
been discussed generally. Our scheme shows that higher order corrections lead
to an effective Hamiltonian with infinite range of interactions.
