Three dimensional finite temperature SU(3) gauge theory near the phase transition

TL;DR

This study investigates the finite temperature phase transition in three-dimensional SU(3) gauge theory, analyzing critical behavior and universality class through lattice simulations and finite size scaling, and compares results with string model predictions.

Contribution

It provides detailed finite size scaling analysis of SU(3) gauge theory near the phase transition, confirming universality class with the 2D three-state Potts model and comparing critical exponents with string model predictions.

Findings

Critical exponents match the 2D three-state Potts model.

Critical temperature closely aligns with Nambu-Goto string model predictions.

Finite size scaling extends measurements to larger lattice sizes.

Abstract

We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent \nu has the mean field value, which is quite different from the value in the abovementioned Potts model. Using our values of the critical couplings we also determine the continuum limit of the value of the critical temperature in terms of the square root of the zero temperature string tension. This value is very near to the prediction of the Nambu-Goto string model in spite of the different critical behaviour.