EFFECTIVE CRITICAL EXPONENTS FOR DIMENSIONAL CROSSOVER AND QUANTUM-SYSTEMS FROM AN ENVIRONMENTALLY FRIENDLY RENORMALIZATION-GROUP

Series for the Wilson functions of an ''environmentally friendly'' ren ormalization group are computed to two loops, for an O(N) vector model , in terms of the ''floating coupling,'' and resummed by the Pade meth od to yield crossover exponents for finite size and quantum systems. T he resulting effective exponents obey all scaling laws, including hype rscaling in terms of an effective dimensionality, d(eff) = 4 - gamma(l ambda), which represents the crossover in the leading irrelevant opera tor, and are in excellent agreement with known results.