arXiv subjects
Publications and source records attributed to I. Montvay.
Nested multi-step stochastic correction offers a possibility to improve updating algorithms for numerical simulations of lattice gauge theories with fermions. The corresponding generalisations of the two-step multi-boson (TSMB) algorithm as well as some applications with hybrid Monte Carlo (HMC) algorithms are considered.
Lattice QCD with Wilson fermions generically shows the phenomenon of a first order phase transition. We study the phase structure of lattice QCD using Wilson twisted mass fermions and the Wilson plaquette gauge action are used in a range of beta values where such a first order phase transition is observed. In particular, we investigate the dependence of the first order phase transition on the value of the lattice spacing. Using only data in one phase and neglecting possible problems arising from the phase transition we are able to perform a first scaling test for physical quantities using this action.
The effect of changing the lattice action for the gluon field on the recently observed [1] first order phase transition near zero quark mass is investigated by replacing the Wilson plaquette action by the DBW2 action. The lattice action for quarks is unchanged: it is in both cases the original Wilson action. It turns out that Wilson fermions with the DBW2 gauge action have a phase structure where the minimal pion mass and the jump of the average plaquette are decreased, when compared to Wilson fermions with Wilson plaquette action at similar values of the lattice spacing. Taking the DBW2 gauge action is advantageous also from the point of view of the computational costs of numerical simulations.
The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable when the untwisted quark mass assumes positive or negative values. We provide interpretations of this phenomenon in terms of chiral symmetry breaking and the effective potential model of Sharpe and Singleton.
The phase structure of zero temperature twisted mass lattice QCD is investigated. We find strong metastabilities in the plaquette observable when the untwisted quark mass sweeps across zero.
The quark mass dependence of meson masses and decay constants in N_f=2 QCD is studied at a fixed gauge coupling with different dynamical quark masses. Partially Quenched Wilson Chiral Perturbation Theory (PQWchiPT) is applied to obtain the extrapolation to zero quark mass. It is shown, that in our analysis NNLO-terms play a more important role than O(a)-terms, which can be neglected. Also we compare our results with recent CP-PACS results.
Our previous calculations of the sea- and valence-quark mass dependence of the pseudoscalar meson masses and decay constants is repeated on a 16^3x32 lattice which allows for a better determination of the quantities in question. The conclusions are similar as before on the 16^4 lattice [1]. The two light dynamical quark flavours we simulate have masses in the range 1/4 m_s < m_{u,d} < 2/3 m_s. The sea quark mass dependence of f_pi and m_pi^2/m_q is well described by the next-to-leading order (NLO) Chiral Perturbation Theory (ChPT) formulas and clearly shows the presence of chiral logarithms. The valence quark mass dependence requires the presence of NNLO contributions in Partially Quenched ChPT (PQChPT) -- in addition to the NLO terms. The O(a) lattice artifacts in these quantities turn out to be small.
The dependence of pseudo-scalar masses and decay constants on the sea and valence quark masses is investigated in the pseudo-Goldstone boson sector of QCD with two light quark flavours. The sea quark masses are at present in the range ${1/3}m_s \leq m_{ud} \leq {2/3}m_s$ whereas the valence quark masses satisfy ${1/2}m_{sea} \leq m_{val} \leq 2m_{sea}$. The values of the Gasser-Leutwyler low energy constants $L_4$, $L_5$, $L_6$ and $L_8$ are estimated. The computation is done with the Wilson-quark lattice action at gauge coupling $β=5.1$ on $16^4$ lattices. ${\cal O}(a)$ effects are taken into account by applying chiral perturbation theory for the Wilson lattice action as proposed by Rupak and Shoresh.
The dependence of the pseudoscalar meson masses and decay constants on sea and valence quark masses is compared to next-to-leading order (NLO) Chiral Perturbation Theory (ChPT). The numerical simulations with two light dynamical quark flavors are performed with the Wilson-quark lattice action at gauge coupling beta=5.1 and hopping parameters kappa=0.176, 0.1765, 0.177 on a 16^4 lattice. O(a) lattice artifacts are taken into account by applying chiral perturbation theory for the Wilson lattice action. The values of the relevant combinations of Gasser-Leutwyler constants L_4, L_5, L_6 and L_8 are estimated.
The dependence of the pseudoscalar meson mass and decay constant is compared to one-loop Partially Quenched Chiral Perturbation Theory (PQChPT) in a numerical simulation with two light dynamical quarks. The characteristic behaviour with chiral logarithms is observed. The values of the fitted PQChPT-parameters are in a range close to the expectation in continuum in spite of the fact that the lattice spacing is still large, namely a=0.28 fm.
A recurrence scheme is defined for the numerical determination of high degree polynomial approximations to functions as, for instance, inverse powers near zero. As an example, polynomials needed in the two-step multi-boson (TSMB) algorithm for fermion simulations are considered. For the polynomials needed in TSMB a code in C is provided which is easily applicable to polynomial degrees of several thousands.
The computational cost of numerical simulations of QCD with light dynamical Wilson-quarks is estimated by determining the autocorrelation of various quantities. In test runs the expected qualitative behaviour of the pion mass and coupling at small quark masses is observed.
We report on the simulation of QCD with light dynamical quarks using the two-step multi-boson (TSMB) algorithm. In an exploratory study with two flavours of quarks at lattice spacing about 0.27 fm and with quark mass down to one sixth of the strange quark mass eigenvalue spectra and autocorrelations have been studied. Here we present results on the volume dependence as well as tests of possible algorithmic improvements.
The computational cost of numerical simulations of QCD with light dynamical Wilson-quarks is estimated. The qualitative behaviour of the pion mass and coupling at small quark masses is discussed.
Two degenerate flavours of quarks are simulated with small masses down to about one fifth of the strange quark mass by using the two-step multi-boson (TSMB) algorithm. The lattice size is 8^3 x 16 with lattice spacing about 0.27fm which is not far from the N_t=4 thermodynamical cross-over line. Autocorrelations of different physical quantities are estimated as a function of the quark mass. The eigenvalue spectra of the Wilson-Dirac operator are investigated.
The numerical simulation of domain wall quarks with the two-step multi-boson (TSMB) algorithm is investigated. Tests are performed on a 8^3*4 lattice with N_f=2 quark flavours.
The numerical simulation of domain wall quarks with the two-step multi-boson (TSMB) algorithm is considered. The inclusion of single quark flavours, as required for strange quarks, is discussed. The usage of computer memory can be kept relatively low, independently of the order of polynomial approximations. Tests are performed with two flavours (N_f=2) of degenerate quarks near the N_t=4 thermodynamical cross over.
We give here the contents pages for the Proceedings of the Lattice 2001 conference (19th International Symposium on Lattice Field Theory) that took place in August 2001 in Berlin, Germany. The contents are in HTML form with clickable links to the papers that exist on the arXiv, mostly in hep-lat. Corrections and comments should be sent to bunk@physik.hu-berlin.de.