Resummation of Cactus Diagrams in Lattice QCD, to all Orders

We show how to perform a resummation, to all orders in perturbation theory, of a certain class of gauge invariant tadpole-like diagrams in Lattice QCD. These diagrams are often largely responsible for lattice artifacts. Our resummation leads to an improved perturbative expansion. Applied to a number of cases of interest, e.g. the lattice renormalization of some two-fermion operators, this expansion yields results remarkably close to corresponding nonperturbative estimates. We consider in our study both the Wilson and the clover action for fermions.Comment: LATTICE99(Improvement and Renormalization), 3 pages, LATeX with eps figures, uses espcrc2.sty. Corrected a statement regarding comparison with other methods. (We thank A. Kronfeld for bringing this point to our attention.

N-ality and topology at finite temperature

We study the spectrum of confining strings in SU(3) pure gauge theory, in different representations of the gauge group. Our results provide direct evidence that the string spectrum agrees with predictions based on n-ality. We also investigate the large-N behavior of the topological susceptibility $\chi$ in four-dimensional SU(N) gauge theories at finite temperature, and in particular across the finite-temperature transition at $T_c$. The results indicate that $\chi$ has a nonvanishing large-N limit for $T<T_c$, as at T=0, and that the topological properties remain substantially unchanged in the low-temperature phase. On the other hand, above the deconfinement phase transition, $\chi$ shows a large suppression. The comparison between the data for N=4 and N=6 hints at a vanishing large-N limit for $T>T_c$.Comment: 3 pages, 2 figures. Presented at Lattice2004(topology

The Critical Hopping Parameter in O(a) improved Lattice QCD

We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $\kappa_c$ coming from Monte Carlo simulations.Comment: 11 pages, 2 EPS figures. The only change with respect to the original version is inclusion of the standard formulae for the gauge fixing and ghost parts of the action. Accepted for publication in Physical Review

Gauge invariant Field Strength Correlators in QCD

Gauge invariant correlators in QCD are studied on the lattice.A Systematic determination of the correlation lengths for gluon field strength correlators and quark correlators is made.The measurement of the gluon and quark condensates is discussed.Comment: 5 pages,4 figures.Presented by A.Di Giacomo to ICHEP98. To appear in the proceedings Misprints correcte

Chateaubriand\u27s Florida and His Journey to America

The American writings of Chateaubriand have nearly been forgotten. Despite the beauty of their poetic prose and the power of their descriptions, historians now consider them obsolete. In 1968 the bicentennial year of his birth was celebrated in other parts of the world with special conferences and impressive publications, but in the United States no periodical commemorated the event, and no paper re-evaluating Chateaubriand’s contribution was read in any of the numerous historical meetings. And yet, Chateaubriand was not just another author. During the first half of the nineteenth century his writings played a great part in shaping French, if not European ideas about America. In the Parisian literary salons, eager young intellectuals tried to satisfy their insatiable curiosity about the New World by listening to his exotic tales. Among them was Alexis de Tocqueville, Chateaubriand’s distance cousin. And long after Chateaubriand’s death in 1848, Europeans who visited this country still carried with them preconceptions and cliches derived from his writings

The Background of the Greek Settlers in the New Smyrna Colony

Andrew Turnbull, the principal founder of the New Smyrna Colony, was not the first who thought of bringing Greeks to people Florida. Immediately after the Treaty of Paris in 1763, which transferred Florida into British hands, William Knox, in a memorial to Whitehall, had already made this suggestion in a very convincing way. Knox, who later was Under-Secretary of State for American Affairs from 1770 to 1782, made, in his memorial, a detailed analysis of conditions and possibilities of the newly acquired Province of Florida. Attempting to solve the urgent problem of peopling this area, completely depopulated after the departure of the Spanish, he had formed the opinion that the nature of the soil and climate and the sort of products which were best adapted to both, pointed to a special kind of settlers who ought to be encouraged to establish themselves in Florida

Lattice effects in the La2−x_{\rm 2-x}Srx_{\rm x}CuO4_{\rm 4} compounds

Systematic Raman studies on several cuprates (YBa$_{\rm 2}$Cu$_{\rm 3}$O$_{\rm x}$, YBa$_{\rm 2}$Cu$_{\rm 4}$O$_{\rm 8}$ or Bi$_{\rm 2}$Sr$_{\rm 2}$CaCu$_{\rm 2}$O$_{\rm 8}$) have shown that at optimal doping the compounds are at the edge of lattice instability; once this level is exceeded, by means of doping or applying external hydrostatic pressure, the changes in the transition temperature are accompanied by spectral modifications. There are strong indications that the reduction in T$_{\rm c}$ is correlated with a separation into nanoscale phases, which involve the oxygen atoms of the CuO$_{\rm 2}$ planes. In this work, modifications with doping in the Raman spectra of the La$_{\rm 2-x}$Sr$_{\rm x}$CuO$_{\rm 4}$ compound are presented, which show that spin or charge ordering is coupled with lattice distortions in the whole doping region.Comment: 6 pages, 6 figure

Resummation of Cactus Diagrams in the Clover Improved Lattice Formulation of QCD

We extend to the clover improved lattice formulation of QCD the resummation of cactus diagrams, i.e. a certain class of tadpole-like gauge invariant diagrams. Cactus resummation yields an improved perturbative expansion. We apply it to the lattice renormalization of some two-fermion operators improving their one-loop perturbative estimates

Three-Loop Results in QCD with Wilson Fermions

We calculate the third coefficient of the lattice beta function in QCD with Wilson fermions, extending the pure gauge results of Luescher and Weisz; we show how this coefficient modifies the scaling function on the lattice. We also calculate the three-loop average plaquette in the presence of Wilson fermions. This allows us to compute the lattice scaling function both in the standard and energy schemes.Comment: 3 pages, LaTeX (fleqn.sty, espcrc2.sty), contribution to Lattice'97. Table caption corrected. The longer write-ups are in hep-lat/9801007 (beta function) and hep-lat/9801003 (plaquette