2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214960Using the path integral method, we calculate the partition function and generating functional (of the field strengths) on the nonlocal generalized 2D Yang - Mills theories ($nlgYM_2$'s), which is nonlocal in auxiliary field [14]. Our calculations is done for general surfaces. We find a general expression for free energy of $W(ϕ) = ϕ^{2k}$ in $nlgYM_2$ theories at the strong coupling phase (SCP) regime ($A > A_c$) for large groups. In the specific $ϕ^4$ model, we show that the theory has a third order phase transition.tex file, no figure. accepted for publication in Eur. Phys. J. C. (2000)High Energy Physics - Theorytext