Topological Invariance at Finite Temperature

TL;DR

This paper investigates the finite-temperature phase transition in a charged vector matter system coupled to a Chern-Simons gauge field, revealing a zeroth-order transition to a topological phase at a critical temperature.

Contribution

It introduces the concept of a zeroth-order phase transition in a Chern-Simons coupled system and analyzes the thermal behavior leading to topological phase change.

Findings

Identification of a critical temperature where effective mass vanishes

Discovery of a zeroth-order phase transition with discontinuous free energy

Application insights to (2+1)D quantum gravity

Abstract

We examine the thermal behavior of a theory with charged massive vector matter coupled to Chern-Simons gauge field. We obtain a critical temperature Tc, at which the effective mass of vector field vanishes, and the system transfers from a symmetry broken phase to topological phase. The phase transition is suggested to be of the zeroth order, as the free energy of the system is discontinuous at Tc. Application to the (2+1) dimensional quantum gravity is briefly discussed.