  Based on our exact effective spin model, the zero temperature $SU(N)$ gauge
field confinement has been studied by the deconfinement-confinement phase
transition order parameter, i.e. the Wilson line, rather than the quark
antiquark potential. The procedure would allow one to study the confinement in
the true continuum limit. For the $(1+1)$ $SU(2)$ gauge field, the confinement
and a linear zero temperature Polyakov quark antiquark potential were shown. It
is also shown, for the first time, that the Polyakov and Wilson potentials are
identical.
