  The renormalization group (RG) flow for the two-dimensional sine-Gordon model
is determined by means of Polchinski's RG equation at next-to-leading order in
the derivative expansion. In this work we have two different goals, (i) to
consider the renormalization scheme-dependence of Polchinski's method by
matching Polchinski's equation with the Wegner-Houghton equation and with the
real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go
beyond the local potential approximation in the gradient expansion in order to
clarify the supposed role of the field-dependent wave-function renormalization.
The well-known Coleman fixed point of the sine-Gordon model is recovered after
linearization, whereas the flow exhibits strong dependence on the choice of the
renormalization scheme when non-linear terms are kept. The RG flow is compared
to those obtained in the Wegner-Houghton approach and in the dilute gas
approximation for the two-dimensional Coulomb-gas.
