Toward an analytic determination of the deconfinement temperature in SU(2) L.G.T.

Abstract

We consider the SU(2) lattice gauge theory at finite temperature in (d+1) dimensions, with different couplings ${\beta }_t$ and ${\beta }_s$ for timelike and spacelike plaquettes. By using the character expansion of the Wilson action and performing the integrals over space-like link variables, we find an effective action for the Polyakov loops which is exact to all orders in ${\beta }_t$ and to the first non-trivial order in ${\beta }_s$. The critical coupling for the deconfinement transition is determined in the (3+1) dimensional case, by the mean field method, for different values of the lattice size $N_t$ in the compactified time direction and of the asymmetry parameter $\rho =\sqrt{{\beta }_t/{\beta }_s}$. We find good agreement with Montecarlo simulations in the range $1\le N_t\le 5$, and good qualitative agreement in the same range with the logarithmic scaling law of QCD. Moreover the dependence of the results from the parameter $\rho$ is in excellent agreement with previous theoretical predictions.

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• Scaling and Asymptotic Scaling in the SU(2) Gauge Theory
• Induced QCD at Large N
• Area Law and Continuum Limit in "Induced QCD"
• Two dimensional QCD is a one dimensional Kazakov-Migdal model
• The Kazakov-Migdal Model as a High Temperature Lattice Gauge Theory
• Deconfinement Transition in Large N Lattice Gauge Theory

Cited by in corpus (15)

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• Relation between the Polyakov loop and the chiral order parameter at strong coupling
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• Inverse Monte-Carlo determination of effective lattice models for SU(3) Yang-Mills theory at finite temperature
• Phase Structure of Z(3)-Polyakov-Loop Models
• The deconfinement transition of finite density QCD with heavy quarks from strong coupling series
• Effective Actions for the SU(2) Confinement-Deconfinement Phase Transition
• Effective lattice theories for Polyakov loops
• Free energy for parameterized Polyakov loops in SU(2) and SU(3) lattice gauge theory
• Equilibrium criterion and effective spin models for finite temperature gauge theories
• $\xi /{\xi }_{2nd}$ ratio as a tool to refine Effective Polyakov Loop models
• Analytic results in 2+1-dimensional Finite Temperature LGT
• The $\xi /{\xi }_{2nd}$ ratio as a test for Effective Polyakov Loop Actions
• Effective Lattice Actions for Finite-Temperature Yang-Mills Theory
• Debye Screening Mass from effective Potentials in Lattice Gauge Theory