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After review the 2D Yang-Mills theories $(YM_{2})$ and its
large-\emph{N} behaviour, the Generalized 2D Yang-Mills theories
$(gYM_{2})$ and their partition functions on a general
two-dimensional Riemann surface are discussed. The large-\emph{N}
behaviour of these models is studied in weak regime, and in strong
regime, we restrict ourselves to $\phi^{4}$ $gYM_{2}$. We show
that this model has a third order phase transition, similar to
ordinary $YM_{2}$ theory.
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