2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/38910Based 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.Latex file, 9 pages. DU-TH-002High Energy Physics - Latticetext