  We consider the sequence of Gibbs measures of Ising models with Kac
interaction defined on a periodic two-dimensional discrete torus near
criticality. Using the convergence of the Glauber dynamic proven by H. Weber
and J.C. Mourrat and a method by H. Weber and P. Tsatsoulis, we show tightness
for the sequence of Gibbs measures of the Ising-Kac model near criticality and
characterise the law of the limit as the $\Phi^4_2$ measure on the torus.
  Our result is very similar to the one obtained by M. Cassandro, R. Marra and
E. Presutti on $\mathbb{Z}^2$, but our strategy takes advantage of the dynamic,
instead of correlation inequalities. In particular, our result covers the whole
critical regime and does not require the large temperature / large mass / small
coupling assumption present in earlier results.
