CROSSOVER SCALING - A RENORMALIZATION-GROUP APPROACH

We derive a theory of crossover scaling based on a scaling variable g xi(g), where g is the anisotropy parameter inducing the crossover and xi(g) is the correlation length in the presence of g. Our consideratio ns are field theoretic and based on a renormalization group with a g d ependent differential generator that interpolates between qualitativel y different degrees of freedom. xi(g) is a nonlinear scaling field for this renormalization group and interpolates between (T-T-c(g))(-nu 0) and (T-T-c(g))(-nu infinity) (nu(0) and nu(infinity) being the isotro pic and anisotropic exponents respectively). By expanding about a 'flo ating' fixed point we can make corrections to scaling small throughout the crossover. In this formulation effective scaling exponents obey s tandard scaling laws, e.g. gamma(eff)=nu(eff)(2-eta(eff)). We discuss its advantages giving for various crossovers explicit supporting pertu rbative calculations of the susceptibility, which is found to conform to the general form derived from the g dependent renormalization group .