We study the ultraviolet stability problem for the two-dimensional Yukawa interaction λ J : cos uφ ξ : dξ in the region 4π < α 2 < α 2 , where 6π < α 2 < 8π. The results have a natural Coulomb gas interpretation, because the counterterms do not depend on the field.

We interpret the results of the preceding paper (I) in terms of partial resummations of the perturbative series for the effective interaction. As an application we sketch how our resummation method leads to a simple summation rule leading to a convergent expansion for the Schwinger functions of the planar Φ^-theory.

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