Precision calculation of magnetization and specific heat of vortex liquids and solids in type II superconductors

A new systematic calculation of magnetization and specific heat contributions of vortex liquids and solids (not very close to the melting line) is presented. We develop an optimized perturbation theory for the Ginzburg - Landau description of thermal fluctuations effects in the vortex liquids. The expansion is convergent in contrast to the conventional high temperature expansion which is asymptotic. In the solid phase we calculate first two orders which are already quite accurate. The results are in good agreement with existing Monte Carlo simulations and experiments. Limitations of various nonperturbative and phenomenological approaches are noted. In particular we show that there is no exact intersection point of the magnetization curves both in 2D and 3D.