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.

• Received 17 September 1999

DOI:https://doi.org/10.1103/PhysRevD.61.085018