arXiv subjects
Publications and source records attributed to P. Marenzoni.
We present the results of two high-statistics studies of the gluon propagator in the Landau gauge, at $β=6.0$, on different lattice volumes. The dependence of the propagator on the momenta is well described by the expression $G(k^2) = \Big[ M^2+Z\cdot k^2(k^2/ Λ^2)^η)\Big]^{-1}$. We obtain a precise determination of $η=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit.
We present the results of a high statistics lattice study of the gluon propagator, in the Landau gauge, at $β=6.0$. As suggested by previous studies, we find that, in momentum space, the propagator is well described by the expression $G(k^2)= \Big[ M^2 + Z\cdot k^2(k^2/Λ^2)^η\Big]^{-1} $. By comparing $G(k^2)$ on different volumes, we obtain a precise determination of the exponent $η=0.532(12)$, and verify that $M^2$ does not vanish in the infinite volume limit. The behaviour of $η$ and $M^2$ in the continuum limit is not known, and can only be studied by increasing the value of $β$.
We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_μ(x) \to \exp\{A_μ(x)/\sqrtβ\}$ into the Langevin algorithm and the observables and to perform the expansion in β^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (β^{-4}) which extends by one loop the previously known series.
We report on a study of the autocorrelation times of the local version of the Hybrid Monte Carlo (LHMC) algorithm for pure gauge $SU(3)$. We compare LHMC to standard multi-hit Metropolis and to the global version of the same HMC. For every algorithm we measure the autocorrelation time for a variety of observables and the string tension as a function of beta. The measurements performed on 8^4 and 16^4 lattices indicate that the autocorrelation time of LHMC is significantly shorter than for the other two algorithms.
We have performed an exhaustive search for Gribov copies on the lattice and their possible dependence from finite temperature effects. We show that, for each value of lattice size, Gribov copies are dense in configuration space at low temperature but their density tend to lower when the temperature increases. We have investigated lattice sizes running from $16^3\times 8$ to $16^4$.