Critical behavior of uniaxial systems with strong dipolar interactions

Abstract
It has been conjectured that uniaxial ferromagnets (or ferroelectrics) with strong dipolar forces should behave in d dimensions as the corresponding system with short-range interactions in d+1 dimensions. It is shown here that this correspondence is not valid. The general theory is outlined and calculations are carried out explicitly up to two-loop order. Corrections to the Larkin-Khmel'nitskii result are derived. They differ from what one would obtain for a four-dimensional short-range system.