We exploit the recent lattice results for the infrared gluon propagator with light dynamical quarks and solve the gap equation for the quark propagator. Chiral symmetry breaking and confinement (intimately tied with the analytic properties of QCD Sch
winger functions) order parameters are then studied.
This letter reports on a new procedure for the lattice spacing setting that takes advantage of the very precise determination of the strong coupling in Taylor scheme. Although it can be applied for the physical scale setting with the experimental val
ue of $Lambda_{overline{rm MS}}$ as an input, the procedure is particularly appropriate for relative calibrations. The method is here applied for simulations with four degenerate light quarks in the sea and leads to prove that their physical scale is compatible with the same one for simulations with two light and two heavy flavours.
We present a lattice calculation of the renormalized running coupling constant in symmetric (MOM) and asymmetric ($widetilde{rm MOM}$) momentum substraction schemes including $u$, $d$, $s$ and $c$ quarks in the sea. An Operator Product Expansion domi
nated by the dimension-two $langle A^2rangle$ condensate is used to fit the running of the coupling. We argue that the agreement in the predicted $langle A^2rangle$ condensate for both schemes is a strong support for the validity of the OPE approach and the effect of this non-gauge invariant condensate over the running of the strong coupling.
Gluon and ghost propagators data, obtained in Landau gauge from lattice simulations with two light and two heavy dynamical quark flavours ($N_f$=2+1+1), are described here with a running formula including a four-loop perturbative expression and a non
perturbative OPE correction dominated by the local operator $A^2$. The Wilson coefficients and their variation as a function of the coupling constant are extracted from the numerical data and compared with the theoretical expressions that, after being properly renormalized, are known at ${cal O}(alpha^4)$. As also $Lambda_{msbar}$ is rather well known for $N_f$=2+1+1, this allows for a precise consistency test of the OPE approach in the joint description of different observables.
$LiHo_xY_{1-x}F_4$ is an insulating system where the magnetic Ho$^{3+}$ ions have an Ising character, and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of the ground state for samples
with x=0.25, 0.12, 0.08, 0.045 and 0.018. In contrast with some previous works, we have not found any signature of canonical spin glass behavior down to $approx$15mK. Instead, below $approx$300mK we observed dynamic magnetism characterized by a single correlation time with a temperature independent fluctuation rate. We observed that this low temperature fluctuation rate increases with x up to 0.08, above which it levels off. The 300mK energy scale corresponds to the Ho3+ hyperfine interaction strength, suggesting that the hyperfine interaction may be intimately involved with the spin dynamics in this system.
