The large-N phase transition of lattice SU(N) gauge theories

TL;DR

The paper tackles the large-$N$ phase transition in lattice SU($N$) gauge theories by leveraging the twisted Eguchi-Kawai (TEK) reduced model and a multicanonical Monte Carlo approach to precisely determine the transition temperature. The TEK construction reproduces the large-$N$ Wilson theory's Schwinger-Dyson equations, while the multicanonical sampling, with carefully modeled energy distributions, enables efficient tunneling between coexisting vacua near a first-order transition. The authors find that the inverse transition temperature $\beta_t$ scales linearly with $1/N^2$ and obtain $\beta_t\to 0.3596(2)$ as $N\to\infty$, confirming the large-$N$ first-order nature and providing a precise benchmark. Overall, the work validates TEK as a practical tool for nonperturbative, large-$N$ gauge dynamics and demonstrates the effectiveness of multicanonical sampling for lattice phase transitions.

Abstract

We investigate the large-N phase transition of lattice SU(N) gauge theories in the Wilson formulation, by performing a Monte Carlo simulation of the twisted Eguchi-Kawai model. A variant of the multicanonical algorithm allows a detailed exploration of the phase transition and a precise determination of the transition temperature.

Figures (3)

• Figure 1: The Monte Carlo time evolution of the energy, using the M2 algorithm for $N=64$.
• Figure 2: The (unnormalized) energy distribution $\rho$, compared with a best fit to Eq. (\ref{['BLimp']}).
• Figure 3: Linear fit in $1/N^2$ to $\beta_t$. The solid line is a fit excluding the rightmost point ($N=25$); the dashed line is a fit including all the four points plotted.