Determining the order of SU(3) deconfining phase transition

TL;DR

This paper derives an effective spin model for finite temperature SU(3) gauge theory, confirming that the deconfining phase transition is first order with only nearest neighbor interactions.

Contribution

It introduces a simplified effective spin model showing that only nearest neighbor coupling is relevant for the SU(3) deconfining transition.

Findings

The effective model confirms the first order nature of the transition.

Only nearest neighbor interactions are significant in the model.

Results align with previous numerical studies.

Abstract

An effective spin model for the finite temperature non-abelian lattice gauge theory is derived. The outcome is the surprising result that only nearest neighbor coupling survives, thus confirming the well known numerical results that the deconfining phase transition of the (3+1)-dimensional $SU(3)$ pure gauge theory is first order.