The deconfining phase transition in D=2+1 SU(N) gauge theories

TL;DR

The paper analyzes deconfinement transitions in 2+1D SU(N) gauge theories (N=2..8) using lattice simulations to determine transition order and continuum behavior. It establishes a clear N-dependent pattern: second-order transitions for N≤3 and first-order for N≥5, with SU(4) appearing weakly first-order. By extrapolating to the continuum and applying large-N scaling, the authors show that $T_c/\sqrt{\sigma}$ is well described across all N by $T_c/\sqrt{\sigma} = 0.9026(23) + 0.880(43)/N^2$, and they analyze latent heat and finite-volume effects, finding $L_h$ grows like $N^2$ and finite-volume corrections scale as $1/N^2$ at large N. The results parallel the 3+1D case, offering a coherent view of deconfinement physics across dimensions and reinforcing large-N expectations for gauge theories.

Abstract

We study the deconfining transition of SU(N) gauge theories in 2+1 dimensions for N ranging between N=2 and N=8. We confirm that the transition is second order for N<4 and first order for N>4. For the more delicate case of SU(4) all our evidence points to the transition being weakly first order. After extrapolating to the continuum limit, we obtain a deconfining temperature that can be well fitted by Tc/sqrt(sigma) = 0.9026(23) + 0.880(43)/N^2 for all N.

Figures (12)

• Figure 1: An example of reweighting: the Polyakov loop susceptibility $\chi/V$ versus $\beta$ in SU(6) on a $25^2 3$ lattice.
• Figure 2: Number of lattice fields, $N$, with a given value of the Polyakov loop $|\overline{l}_p|$. In SU(2), at $\beta=4.9$, on a $90^2 3$ lattice.
• Figure 3: A plot of the critical coupling $\beta_c(V)$ against $(L_s/L_t)^{-1/\nu}$ with an extrapolation to $V=\infty$. In SU(2) for $aT_c=1/L_t=1/3$.
• Figure 4: Number of lattice fields, $N$, with a given value of the Polyakov loop $|\overline{l}_p|$. In SU(8), at $\beta=82.5$, on a $20^2 3$ lattice.
• Figure 5: A plot of the critical coupling $y=\beta_c(V)$ against $x=(L_s/L_t)^2$ with an extrapolation to $V=\infty$. In SU(6) for $aT_c=1/L_t=1/3$.