  We study the stochastic Allen-Cahn equation driven by a noise term with
intensity $\sqrt{\varepsilon}$ and correlation length $\delta$ in two and three
spatial dimensions. We study diagonal limits $\delta, \varepsilon \to 0$ and
describe fully the large deviation behaviour depending on the relationship
between $\delta$ and $\varepsilon$.
  The recently developed theory of regularity structures allows to fully
analyse the behaviour of solutions for vanishing correlation length $\delta$
and fixed noise intensity $\varepsilon$. One key fact is that in order to get
non-trivial limits as $\delta \to 0$, it is necessary to introduce diverging
counterterms. The theory of regularity structures allows to rigorously analyse
this renormalisation procedure for a number of interesting equations.
  Our main result is a large deviation principle for these renormalised
solutions. One interesting feature of this result is that the diverging
renormalisation constants disappear at the level of the large deviations rate
function. We apply this result to derive a sharp condition on $\delta,
\varepsilon$ that guarantees a large deviation principle for diagonal schemes
$\varepsilon, \delta \to 0$ for the equation without renormalisation.
