Dynamic universality for Z2 and Z3 lattice gauge theories at finite temperature.

Abstract

Swendsen-Wang random surface dynamics for ${Z}_{2}$ and ${Z}_{3}$ gauge theories in 2+1 dimensions is applied to the finite-temperature deconfining transition, and the static universality conjecture of Svetitsky and Yaffe is extended to the exponent $z$ for critical dynamics. Our new dynamic universality conjecture (${z}_{\mathrm{RS}}^{d+1}={z}_{\mathrm{SW}}^{d}$) is supported both by a qualitative argument and by numerical simulations that show that the dynamic critical exponents for (2+1)-dimensional gauge theories (logarithmic or ${z}_{\mathrm{RS}}<0.3\ifmmode\pm\else\textpm\fi{}0.1 \mathrm{and} 0.53\ifmmode\pm\else\textpm\fi{}0.03$ for ${Z}_{2}$ and ${Z}_{3}$, respectively) are consistent with the values for the two-dimensional Ising-Potts models (logarithmic or ${z}_{\mathrm{SW}}=0.20\ensuremath{-}0.27 \mathrm{and} 0.55\ifmmode\pm\else\textpm\fi{}0.03$ for ${Z}_{2}$ and ${Z}_{3}$, respectively) at the finite-temperature transition.