  We consider scalar field theories in dimensions lower than four in the
context of the Wegner-Houghton renormalization group equations (WHRG). The
renormalized trajectory makes a non-perturbative interpolation between the
ultraviolet and the infrared scaling regimes. Strong indication is found that
in two dimensions and below the models with polynomial interaction are always
non-perturbative in the infrared scaling regime. Finally we check that these
results do not depend on the regularization and we develop a lattice version of
the WHRG in two dimensions.
