Nonperturbative flow equations from running expectation values.

We show that Wegner's flow equations, as recently discussed in the Lipkin model, can be solved self-consistently. This leads to a nonlinear differential equation which fully determines the order parameter as a function of the dimensionless coupling constant, even across the phase transition. Since we consider an expansion in the fluctuations, rather than the conventional expansion in the coupling constant, convergence to the exact results is found in both phases when taking the thermodynamic limit.