  A non-perturbative effect in $\kappa$ (renormalized string coupling) obtained
from the large order behavior in the vicinity of the prototypical
Argyres-Douglas critical point of $su(2)$, $N_f =2$, $\mathcal{N} =2$ susy
gauge theory can be studied in the GWW unitary matrix model with the log term:
the one as the work done against the barrier of the effective potential by a
single eigenvalue lifted from the sea and the other as a non-perturbative
function contained in the solutions of the nonlinear differential equation PII
that goes beyond the asymptotic series.
  The leading behaviors are of the form $\exp (-\frac{4}{3}\frac{1}{\kappa} \,
(1, \left(\frac{s}{K}\right)^{\frac{3}{2}} ))$ respectively.
  We make comments on their agreement.
