$\eps$ expansion analysis of very weak first-order transitions in the   cubic anisotropy model: Part I
  The cubic anisotropy model provides a simple example of a system with an arbitrarily weak first-order phase transition. We present an analysis of this model using $\eps$-expansion techniques with results up to next-to-next-to-leading order in $\eps$. Specifically, we compute the relative discontinuity of various physical quantities across the transition in the limit that the transition becomes arbitrarily weakly first-order. This provides a useful test-bed for the application of the $\eps$ expansion in weakly first-order transitions. 
Peter Arnold and Laurence G. Yaffe