Lattice Topological Field Theory and First Order Phase Transition

Carrying out perturbations around a lattice topological field theory in two dimensions, we show that it is on a first order phase transition fixed point with multiplicity ${n(n-1)/2}$, where $n$ is the number of its independent physical observables. We discuss about the order parameters and the finite size effect for the free energy. The finite size effect is described by the topological field theory. We investigate also the renormalization group flow near the fixed point, and show that the flow agrees with that of the Nienhuis-Nauenberg criterion.