Vortex critical behavior at the de-confinement phase transition

TL;DR

This paper investigates the de-confinement phase transition in SU(2) Yang-Mills theory through vortex percolation, revealing critical behavior consistent with the 3D Ising model.

Contribution

It introduces a vortex-based perspective to analyze the de-confinement transition and establishes a connection with the 3D Ising universality class.

Findings

Percolation transition temperature matches the thermal critical temperature.

Finite size scaling function aligns with 3D Ising model predictions.

Critical index of the scaling function is consistent with 3D Ising universality.

Abstract

The de-confinement phase transition in SU(2) Yang-Mills theory is revisited in the vortex picture. Defining the world sheets of the confining vortices by maximal center projection, the percolation properties of the vortex lines in the hypercube consisting of the time axis and two spatial axis are studied. Using the percolation cumulant, the temperature for the percolation transition is seen to be in good agreement with the critical temperature of the thermal transition. The finite size scaling function for the cumulant is obtained. The critical index of the finite size scaling function is consistent with the index of the 3D Ising model.