MULTISCALE SUBTRACTION SCHEME AND PARTIAL RENORMALIZATION-GROUP EQUATIONS IN THE O(N)-SYMMETRICAL PHI(4) THEORY

To resum large logarithms in multiscale problems a generalization of t he <(MS)over bar> is introduced allowing for as many renormalization s cales as there are generic scales in the problem. In the new ''minimal multiscale subtraction scheme'' standard perturbative boundary condit ions become applicable. However, the multiscale beta functions depend on the various renormalization scale ratios and a large logarithms res ummation has to be performed on them. Using these improved beta functi ons the ''partial'' renormalization group equations corresponding to t he renormalization point independence of physical quantities allows on e to resum the logarithms. As an application the leading and next-to-l eading order two-scale analysis of the effective potential in the O(N) -symmetric phi(4) theory is performed. This calculation indicates that there is no stable vacuum in the broken phase of the theory for 1<N l ess than or equal to 4.