In this talk we discussed about the process of smearing out the gauge configurations, technically speaking we don't change the original configurations (as doing so will result in changing probability distribution on which original gauge configurations were generated ) (we just change the way we observe the measurable/correlators).
Smearing involves averaging the link with 3 link staples, averaging(link + linkof(plaq-link)). In this way our links become fat links, and we thus have less distance for correlators to calculate. To find correlators for bigger distance we need larger lattice, or we can just use wilson flow equation to go from UV to IR.
So for project of string tension we have to do smearing to gauge fields (technically we need to change how we measure wilson loop), in continumm limit this will give us original wilson loop.
These are all done to improve the signal to noise ratio (or to get better signal), In below link you can see that the wilson loop value for some node of gpu (try20 ,l32f21b6285), we get average value less then the actual value. i.e. signal is lost in fluctuations. To get rid of it we follow the technique of smearing.
Need for smearing_calculations
lattice QCD action= Actual QCD action + a(some terms) + a^2 (some terms) + .............
In limit a(lattice spacing) --> 0, Lattice QCD describes continumm QCD. That happens at very small value of 'a'. Lattice QCD is like UV cut off. (at very high momentum or small lenght scales we put some cut off), and continumm QCD is like IR (Infra Red limit cut off).
Wilson flow is differential equation of gauge configurations/fields in fictitious time which takes configurations/field from UV to IR (continumm limit of LQCD or QCD).
In lattice QCD, smearing techniques are employed to improve the behavior of the quark and gluon fields on the lattice. These techniques help to reduce the impact of discretization artifacts and enhance the signal-to-noise ratio in numerical simulations. Here are some commonly used smearing techniques in lattice QCD:
APE (Averaged Plaquette Ensemble) smearing involves replacing the link variables on the lattice with a combination of the original links and the average of neighboring links. It is a local smearing technique that helps to reduce lattice artifacts and improve the signal for physical observables.
HYP smearing is a non-abelian smearing technique that involves replacing link variables with a linear combination of the original link and its staples (plaquettes sharing a common link). HYP smearing is known for its ability to enhance the ground-state signal.
Gaussian smearing involves convolving the gauge field configurations with a Gaussian function. It is a non-local smearing technique that helps to enhance the ground-state signal and reduce contamination from excited states.
Wuppertal smearing is a non-abelian smearing technique similar to APE smearing, but it employs a different smearing function. It is designed to suppress high-frequency noise and improve the signal for physical observables.
Jacobi smearing involves applying multiple iterations of a Jacobi-type relaxation procedure to the gauge links. It is a non-local technique that can be used to improve the signal-to-noise ratio.
Stout smearing is a non-abelian smearing technique that involves replacing the link variables with a combination of the original link and a staple term. It is designed to reduce lattice artifacts and enhance the signal for physical observables.
There are various APE-style variants, including improved versions of APE smearing with modified smearing functions or additional parameters to optimize the performance.
Exponential smearing involves replacing the gauge links with an exponential of the original links. It is another non-local smearing technique used to reduce lattice artifacts.
These smearing techniques aim to improve the ground-state signal and reduce contamination from excited states in lattice QCD simulations. The choice of smearing technique often depends on the specific observables being studied and the desired properties of the gauge field configurations
QCD critical point is conjecture critical point happens at real chemical potential.
- we are finding critical point for real chemical potential. some observales diverge at critical point(critical point is 2nd order phase transition), in going from left to right (on real chemical potential), we see that transition shifts from crossover to higher order to second order and to first order.