Universality in finite temperature lattice QCD

Abstract

In the lattice regularization of QCD, physical results must be independent of the choice of lattice action. Finite temperature thermodynamics provides a ve~ sensitive test of this universality, providing a functional comparison between the predictions of different actions. We study thermodynamics using Wilson's. Manton's and Villain's actions as well as the mixed fundamental-adjoint form of Bhanot and Crcutz. Our resalts support universality in all cases, but indicate that in general the region of couplings in present lanicc calculation.,, requires the inclusion of higher order effects in the perturbativc solution of the renormalization group equation.

Z2 monopoles, vortices and the universality of the SU(2) deconfinement transition

“…Such qualitative violations must be distinguished from the quantitative violations of universality found earlier in [17]. The latter disappear as the lattice spacing is reduced to zero and higher order corrections in g 2 u are included [18,19,20]. This will obviously not be the case for any qualitative disagreements like the one mentioned above for the universality of the SU(2) deconfinement transition with the Ising model.…”

Finite-temperature phase transition in SU(2) lattice gauge theory with extended action

“…(5) by a factor of ∼3.5 in a Monte Carlo determination [9] from the ratio of string tension evaluated on β A =constant lines around (1.5, 0.9) and (2.2, 0.0) in the (β, β A )-plane. It was later shown [4] that the θ dependance of this factor further differs rather strongly from eq. (5) on the β A = 0.9 line.…”

“…(4)(5). To avoid big finite spatial volume effects, one chooses N σ > N τ for finite temperature simulations.…”

“…Dimensionless ratios of physical quantities, such as M G / √ σ [2], or T c / √ σ [3], where M G is the lightest glueball mass, T c is the deconfinement temperature and σ is the string tension, have been computed for the SU(2) lattice gauge theory and shown to be almost independent of the lattice actions used. Even more stringently, functions of such dimensionless ratios, e.g., the energy density as a function of T /T c , have been successfully used to demonstrate [4] universality. While these results have boosted our confidence in the existence of a non-perturbative continuum limit of the SU(2) gauge theory, it is still not clear whether more qualitative aspects of the theory, such as the order of the deconfinement phase transition, also exhibit this universality.…”

More on the SU(2) deconfinement transition in the mixed action

“…The early simulations of the SU(2) lattice gauge theory are known to have yielded quantitative violations of universality [18]. However, attributing them to the ignored higher orders in g 2 u , it has been shown [19][20][21] that dimensionless ratios of physical quantities have much weaker such violations. Indeed, one can hope that these violations will smoothly disappear under the error bars of the simulations as the cut-off becomes smaller.…”