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We give a rigorous nonperturbative construction of a massless discretetrajectory for Wilson's exact renormalization group. The model is a threedimensional Euclidean field theory with a modified free propagator. Thetrajectory realizes the mean field to critical crossover from the ultravioletGaussian fixed point to an analog recently constructed by Brydges, Mitter andScoppola of the Wilson-Fisher nontrivial fixed point.Comment: 57 pages, Latex, 2 figures and 3 references adde

A Complete Renormalization Group Trajectory Between Two Fixed Points