  We compute the planar limit of both the free energy and the expectation value
of the $1/2$ BPS Wilson loop for four dimensional ${\cal N}=2$ superconformal
quiver theories, with a product of SU($N$)s as gauge group and bi-fundamental
matter. Supersymmetric localization reduces the problem to a multi-matrix
model, that we rewrite in the zero-instanton sector as an effective action
involving an infinite number of double-trace terms, determined by the relevant
extended Cartan matrix. We find that the results, as in the case of
$\mathcal{N}=2$ SCFTs with a simple gauge group, can be written as sums over
tree graphs. For the $\widehat{A_1}$ case, we find that the contribution of
each tree can be interpreted as the partition function of a generalized Ising
model defined on the tree; we conjecture that the partition functions of these
models defined on trees satisfy the Lee-Yang property, i.e. all their zeros lie
on the unit circle.
