[Paper Review] The Deconfinement Transition on Coarse Lattices

D. W. Bliss, K. Hornbostel+1 more|ArXiv.org|May 31, 1996

Advanced Algebra and Logic1 references3 citations

TL;DR

This paper investigates the deconfinement phase transition in pure Yang-Mills theory using coarse lattice QCD with $N_t = 2, 3, 4$ and lattice spacings from 0.15 fm to 0.33 fm. Employing a perturbatively improved gluon action to suppress $a^2$ and $\alpha_s a^2$ discretization errors, the authors find that the critical temperature $T_c$, when normalized to the charmonium 1P--1S splitting or the torelon mass, shows no significant dependence on the lattice spacing within 5%, indicating good scaling behavior on coarse lattices.

ABSTRACT

We compute the critical temperature $T_c$ for the deconfinement transition of pure QCD on coarse lattices, with $N_t = 2, 3, 4$, and lattice spacings from .33 fm to .15 fm. We employ a perturbatively improved gluon action designed to remove order $a^2$ and $α_s a^2$ errors. We find that $T_c$ in units of the charmonium 1P--1S splitting and the torelon mass is independent of $a$ to within approximately 5\%.

Motivation & Objective

• To determine the critical temperature $T_c$ for the deconfinement transition in pure QCD on coarse lattices with $N_t = 2, 3, 4$.
• To assess the scaling behavior of $T_c$ with respect to lattice spacing by using a perturbatively improved gluon action.
• To evaluate whether $T_c$ normalized to hadronic scales (charmonium 1P--1S splitting and torelon mass) remains independent of the lattice spacing.
• To test the reliability of coarse lattice simulations for studying the deconfinement transition in QCD.

Proposed method

• The study employs a perturbatively improved gluon action designed to remove $\mathcal{O}(a^2)$ and $\mathcal{O}(\alpha_s a^2)$ discretization errors.
• Simulations are performed on lattices with temporal extent $N_t = 2, 3, 4$, corresponding to lattice spacings from 0.15 fm to 0.33 fm.
• The deconfinement transition is identified via the behavior of the Polyakov loop and related observables.
• The critical temperature $T_c$ is extracted from the peak in the susceptibility of the Polyakov loop.
• Normalization of $T_c$ is performed using the charmonium 1P--1S splitting and the torelon mass as reference scales.
• Statistical analysis and error estimation are performed to assess the consistency of $T_c$ across different lattice spacings.

Experimental results

Research questions

• RQ1 Does the critical temperature $T_c$ for the deconfinement transition in pure QCD remain stable when lattice spacing is varied on coarse lattices?
• RQ2 To what extent do $\mathcal{O}(a^2)$ and $\mathcal{O}(\alpha_s a^2)$ discretization errors affect the determination of $T_c$ on coarse lattices?
• RQ3 Is $T_c$ normalized to hadronic scales (e.g., charmonium 1P--1S splitting or torelon mass) independent of the lattice spacing?
• RQ4 Can a perturbatively improved gluon action effectively suppress lattice artifacts in the deconfinement transition region?

Key findings

• The critical temperature $T_c$, when normalized to the charmonium 1P--1S splitting, shows no significant dependence on the lattice spacing within approximately 5%.
• Similarly, $T_c$ normalized to the torelon mass remains nearly constant across different lattice spacings, indicating good scaling behavior.
• The use of a perturbatively improved gluon action successfully suppresses $\mathcal{O}(a^2)$ and $\mathcal{O}(\alpha_s a^2)$ errors, supporting the reliability of coarse lattice results.
• The results suggest that coarse lattices with $N_t = 2, 3, 4$ can yield consistent and reliable estimates of $T_c$ when appropriate actions are used.
• The observed insensitivity of normalized $T_c$ to lattice spacing supports the validity of continuum extrapolation using coarse lattices for the deconfinement transition.