Scaling properties of the energy density in SU(2) lattice gauge theory

Abstract

The lattice data for the energy density of SU (2) gauge theory are calculated with non-perturbative derivatives of the coupling constants. These derivatives are obtained from two sources : i) a parametrization of the non-perturbative beta function in accord with the measured critical temperature and ∆β−values and ii) a non-perturbative calculation of the presssure. We then perform a detailed finite size scaling analysis of the energy density near T c . It is shown that at the critical temperature the energy density is scaling as a function of V T 3 with the corresponding 3d Ising model critical exponents. The value of ǫ(T c )/T 4 c in the continuum limit is estimated to be 0.256(23). In the high temperature regime the energy density is approaching its weak coupling limit from below, at T /T c ≈ 2 it has reached only about 70% of the limit.

Magnetic Monopoles in the Deconfined Phase of Yang-Mills Theories

“…The physical scale has been determined according to a(β )Λ L = R(β )λ (β ), where R is the two-loop perturbative β -function, while λ is a non-perturbative correction factor computed and reported in Ref. [25]. We have assumed the values T c /Λ L = 21.45(14) [25], T c / √ σ = 0.69(2) [26] and √ σ ≃ 430 MeV.…”

QCD thermodynamics with improved actions

“…Only recently calculations with the standard Wilson action could be extended to lattices with sufficiently large temporal extent (N τ = 6 and 8) that would allow an extrapolation of lattice results for bulk thermodynamic quantities to the continuum limit [18,19]. Computationally the step from N τ = 4 to N τ = 8 is quite non trivial as the computer time needed to achieve numerical results with the same statistical significance on a two times larger lattice increases roughly like 2 10 .…”

β function and equation of state for QCD with two flavors of quarks

“…It was rst used in the context of lattice QCD to calculate the interface tension by S. Huang et al [5] and later modi ed for the bulk pressure of pure gauge QCD by J. Engels et al [6]. The disadvantage of the integral method is that for the pressure at a single temperature and quark mass, a number of di erent simulations are required in order to provide the integrand.…”