  A systematic calculation of magnetization and specific heat contributions due
to fluctuations of vortex lattice in strongly type II superconductors to
precision of 1% is presented. We complete the calculation of the two loop low
temperature perturbation theory by including the umklapp processes. Then the
gaussian variational method is adapted to calculation of thermodynamic
characteristics of the 2D and the 3D vortex solids in high magnetic field.
Based on it as a starting point for a perturbation theory we calculate the
leading correction providing simultaneously an estimate of precision. The
results are compared to existing nonperturbative approaches.
