Three-Loop Ground-State Energy of O(N)-Symmetric Ginzburg-Landau Theory Above T_c in 4-epsilon Dimensions with Minimal Subtraction

As a step towards deriving universal amplitude ratios of the superconductive phase transition we calculate the vacuum energy density in the symmetric phase of O(N)-symmetric scalar QED in D=4-epsilon dimensions in an epsilon-expansion using the minimal subtraction scheme commonly denoted by MS-bar. From the diverging parts of the diagrams, we obtain the renormalization constant of the vacuum Z_v which also contains information on the critical exponent alpha of the specific heat. As a side result, we use an earlier two-loop calculation of the effective potential (H.K. and B.VdB., Phys.Rev. E63 (2001) 056113, cond-mat/0104102) to determine the renormalization constant of the scalar field Z_phi up to two loops.