Lattice Topological Field Theory and First Order Phase Transition

TL;DR

This paper analyzes a two-dimensional lattice topological field theory, revealing it resides at a first order phase transition point with specific multiplicity, and explores its order parameters, finite size effects, and renormalization group flow.

Contribution

It demonstrates that perturbations around a lattice topological field theory lead to a first order phase transition fixed point with a specific multiplicity and characterizes its finite size effects and RG flow.

Findings

Identifies the fixed point as a first order phase transition with multiplicity n(n-1)/2.

Describes finite size effects using topological field theory.

Shows RG flow aligns with Nienhuis-Nauenberg criterion.

Abstract

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.