QUASITOPOLOGICAL FIELD-THEORIES IN 2 DIMENSIONS AS SOLUBLE MODELS

We study a class of lattice field theories in two dimensions that incl udes Yang-Mills and generalized Yang-Mills theories as particular exam ples. Given a two-dimensional orientable surface of genus g, the parti tion function Z is defined for a. triangulation consisting of n triang les of size epsilon. The reason these models are called quasitopologic al is that Z depends on g, n and epsilon but not on the details of the triangulation. They are also soluble in the sense that the computatio n of their partition functions for a two-dimensional lattice can be re duced to a soluble one-dimensional problem. We show that the continuum limit is well defined if the model approaches a topological field the ory in the zero area limit, i.e. epsilon --> 0 with finite n. We also show that the universality classes of such quasitopological lattice fi eld theories can be easily classified.