In the past years a good comprehension of the infrared gluon propagator has been achieved, with a good qualitative agreement between lattice results and Dyson-Schwinger equations. However, lattice simulations have been performed at physical volumes w
hich are close to 20 fm but using a large lattice spacing. The interplay between volume effects and lattice spacing effects has not been investigated. Here we aim to fill this gap and address how the two effects change the gluon propagator in the infrared region. Furthermore, we provide infinite volume extrapolations which take into account the finite volume and finite lattice spacing. We also report on preliminary results for the gluon propagator at finite temperature.
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow Hamiltonian $til
de{H}$. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation.
We show how to improve the molecular dynamics step of Hybrid Monte Carlo, both by tuning the integrator using Poisson brackets measurements and by the use of force gradient integrators. We present results for moderate lattice sizes.
We present initial results of the use of Force Gradient integrators for lattice field theories. These promise to give significant performance improvements, especially for light fermions and large lattices. Our results show that this is indeed the cas
e, indicating a speed-up of more than a factor of two, which is expected to increase as the integration step size becomes smaller for larger lattices and smaller fermion masses.
We discuss how the integrators used for the Hybrid Monte Carlo (HMC) algorithm not only approximately conserve some Hamiltonian $H$ but exactly conserve a nearby shadow Hamiltonian (tilde H), and how the difference $Delta H equiv tilde H - H $ may be
expressed as an expansion in Poisson brackets. By measuring average values of these Poisson brackets over the equilibrium distribution $propto e^{-H}$ generated by HMC we can find the optimal integrator parameters from a single simulation. We show that a good way of doing this in practice is to minimize the variance of $Delta H$ rather than its magnitude, as has been previously suggested. Some details of how to compute Poisson brackets for gauge and fermion fields, and for nested and force gradient integrators are also presented.
