  The Ising ferromagnetic model on a square lattice is revisited using the
Galam Unifying Frame (GUF), set to investigate the dynamics of two-state
variable systems within the frame of opinion dynamics. When combined with
Metropolis dynamics, an unexpected intermediate "dis/order" phase is found with
the coexistence of two attractors associated respectively to an ordered and a
disordered phases. The basin of attraction of initial conditions for the
disordered phase attractor starts from zero size at a first critical
temperature $T_{c1}$ to embody the total landscape of initial conditions at a
second critical temperature $T_{c2}$ with $T_{c1}\approx 1.59$ and
$T_{c2}\approx 2.11$ in $J/k_B$ units. It appears that $T_{c2}$ is close to the
Onsager result $T_{c}\approx 2.27$. The transition, which is first-order like,
exhibits a vertical jump to the disorder phase at $T_{c2}$, reminiscent of the
rather abrupt vanishing of the corresponding Onsager second order transition.
However, using Glauber dynamics combined with GUF does not yield the
intermediate phase and instead the expected single transition at $T_{c}\approx
3.09$. Accordingly, although the "dis/order" phase produced by the GUF -
Metropolis combination is not physical, it is an intriguing result to be
understood. In particular the fact that Glauber and Metropolis dynamics yield
so different results using GUF needs an explanation. The possibility of
extending GUF to larger clusters is discussed.
