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The large-N behavior of the quartic-cubic generalized two dimensionalYang-Mills U(N) on the sphere is investigated for finite cubic couplings.First, it is shown that there are two phase transitions one of which is thirdorder and the other one is second order. Second, $gYM_2$ and Maxwellconstruction are compared and a relationship between two-dimensionalspace-time, that is purely mathematical, and four-dimensional space-time isobtained.

Phase transition of generalized two dimensional Yang-Mills U(N) on the sphere for $G(z)=z^4+\lambda\,z^3$ and Maxwell construction