Abstract
The purpose of this paper is to obtain the logarithmic critical singularities for uniaxial dipolar systems (or for the four dimensional theory) in non zero external field. The result takes a simple form only for n = 1, n being the number of components of the order parameter. For example the inverse magnetic susceptibility behaves as χ-1 ∼ χ -1m.f. | log χ-1m.f. |-1/3 in which m.f. refers to mean field value when H is non zero

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