  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.
