Nonlinear Solutions of Renormalization-Group Equations

We give the first nonlinear solution of renormalization-group equations. This solution, based on the differential generator of Wegner and Houghton, exhibits an explicit mixing of (or crossover between) critical and mean-field behavior. The solution is given for all values of the spin dimension $n$ and to first order in $\epsilon \equiv 4-d$, where $d$ is the lattice dimensionality.