Infrared Renormalons and Finite Volume

We analyze the perturbative expansion of a condensate in the O(N) non-linear sigma model for large N on a two dimensional finite lattice. On an infinite volume this expansion is affected by an infrared renormalon. We extrapolate this analysis to the case of the gluon condensate of Yang-Mills theory and argue that infrared renormalons can be detected by performing perturbative studies even on relatively small lattices.Comment: LaTeX file, 6 figures in postscrip

Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques

Two-dimensional CP**(N-1) models are used to compare the behavior of different cooling techniques on the lattice. Cooling is one of the most frequently used tools to study on the lattice the topological properties of the vacuum of a field theory. We show that different cooling methods behave in an equivalent way. To see this we apply the cooling methods on classical instantonic configurations and on configurations of the thermal equilibrium ensemble. We also calculate the topological susceptibility by using the cooling technique.Comment: 24 pages, 10 figures (from 16 eps files

Sbacchiite, Ca2AlF7, a new fumarolic mineral from the Vesuvius volcano, Napoli, Italy

The new mineral sbacchiite (IMA 2017-097), Ca2AlF7, was found in a fossil fumarole (1944 eruption, T 80 C) at the rim of the crater of the Vesuvius volcano, Napoli, Italy, associated with gearsksutite, usovite, creedite and opal. It forms elongated crystals up to about 60 lm in length. On the basis of powder X-ray diffraction data and chemical analysis, the mineral was recognized to be identical to the corresponding synthetic phase. Crystals are transparent or translucent and colourless, with vitreous lustre and white streak. The tenacity is brittle. The measured density is 3.08(2) g/cm3, the calculated density is 3.116 g/cm3. The empirical formula, (based on 10 atoms per formula unit, apfu) is Ca2.02Mg0.03Al0.99F6.97. Sbacchiite is orthorhombic, space group Pnma, with a = 7.665(2), b = 6.993(1), c = 9.566(2) \uc5, V = 512.2(2) \uc53 and Z = 4. The eight strongest X-ray powder diffraction lines are [dobs \uc5(I)(hkl)]: 3.840(45)(200), 3.563(85)(201), 3.499(100)(020), 2.899(55)(013), 2.750(30)(212), 2.281(20)(104), 2.255(52)(302) and 2.173(36)(131). The structure was refined to R = 0.0479 for 457 reflections with I > 2r(I). The asymmetric unit contains one Al3+ and two independent Ca2+ cations and five fluorine anions. Aluminium is octahedrally coordinated by six fluorine atoms; the arrangement of F around the 7-coordinated Ca(1) conforms to a distorted pentagonal bipyramid and that around Ca(2) to a very distorted polyhedron (in 7 + 1 coordination). All the fluorine atoms are threefold coordinated. The structure framework shows \u2018\u2018isolated\u2019\u2019 [AlF6] octahedra, whereas the coordination polyhedra around Ca are linked by common edges [sequence: Ca(1)\u2013Ca(2)\u2013Ca(1). . .] along [010] and the same holds for the connection along [001]. Along [100], however, only the pentagonal bipyramids around Ca(1) are connected by bridging corners

Confinement from Instantons or Merons

In contrast to ensembles of singular gauge instantons, which are well known to fail to produce confinement, it is shown that effective theories based on ensembles of merons or regular gauge instantons do produce confinement. Furthermore, when the scale is set by the string tension, the action density, topological susceptibility, and glueball masses are similar to those arising in lattice QCD.Comment: 3 pages, 5 figures. Talk given at Lattice2004 (topology and confinement) Fermilab June 21-26, 200

Renormalon disappearance in Borel sum of the 1/N expansion of the Gross-Neveu model mass gap

The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally similar to the QCD heavy quark pole mass renormalons, potentially leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the precise vanishing mechanism of such infrared renormalons, which avoids this (only apparent)contradiction, and operates without need of (Borel) summation contour prescription, usually preventing unambiguous separation of perturbative contributions. As a consequence we stress the direct Borel summability of the (1/N) perturbative expansion of the mass gap. We briefly speculate on a possible similar behaviour of analogous non-perturbative QCD quantities.Comment: 16 pp., 1 figure. v2: a few paragraphs and one appendix added, title and abstract slightly changed, essential results unchange

Acmonidesite, a new ammonium sulfate chloride from La Fossa crater, Vulcano, Aeolian Islands, Italy

The new mineral acmonidesite, (NH4,K,Pb2+,Na)9Fe42+(SO4)5Cl8, was found in an active fumarole (fumarole FA, temperature 3c250\ub0C) at La Fossa crater, Vulcano, Aeolian Islands, Sicily, Italy. It occurs on a pyroclastic breccia as brown prismatic crystals up to 0.10 mm long, in association with salammoniac, alunite and adranosite. The mineral is orthorhombic, space group C2221 (no. 20) with a = 9.841(1), b = 19.448(3) c = 17.847(3) \uc5, V = 3415.7(9) \uc53 and Z = 4. The six strongest reflections in the powder X-ray diffraction pattern are: [dobs in \uc5(I)(hkl)] 8.766(100)(110), 1.805(88)(390), 5.178(45)(131), 4.250(42)(221), 2.926(42)(330) and 2.684(32)(261). The empirical formula (based on 28 anions per formula unit [pfu]) is (NH4)5.77K1.42Pb0.62Na1.24Fe3.96Mn0.08S5.04O20.16Cl7.97Br0.08. The idealised formula is (NH4,K,Pb2+,Na)9Fe42+(SO4)5Cl8. The calculated density is 2.551 g cm\u20133. Using single-crystal diffraction data, the structure was refined to a final R(F) = 0.0363 for 4614 independent observed reflections [I > 2\u3c3(I)]. The structure contains two independent, distorted octahedral iron sites, Fe1 and Fe2, with the iron atoms in the 2+ oxidation state, as confirmed by the interatomic distances and bond-valence calculations (2.06 and 1.94 vu, respectively). Fe1 is surrounded by two chlorine atoms and four oxygens of the sulfate ions, with the following average distances (\uc5): Fe1\u2013O 2.125 and Fe1\u2013Cl 2.472; and Fe2 is surrounded by three chlorine atoms and three oxygens of the sulfate ions, with the following average distances (\uc5): Fe2\u2013O 2.110 and Fe2\u2013Cl 2.531. Three independent sulfate anions are also present and are connected with the iron polyhedra to form a three-dimensional structure containing voids occupied by four independent ammonium ions (two of them partially replaced by K+), one Na+/Pb2+ site and one Cl\u2013 ion

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.Comment: 69 pages, Late

Large-N phase transition in lattice 2-d principal chiral models

We investigate the large-N critical behavior of 2-d lattice chiral models by Monte Carlo simulations of U(N) and SU(N) groups at large N. Numerical results confirm strong coupling analyses, i.e. the existence of a large-N second order phase transition at a finite $\beta_c$.Comment: 12 pages, Revtex, 8 uuencoded postscript figure

Ritrovamento di Atacamite in cristalli al Vesuvio

In the small vacuoles of an older lava from one of the quarries of Villa Inglese (Torre del Greco, Napoli) atacamite as crystalline have been discovered. This is a rare event in this volcanic complex

Nuovo ritrovamento di corindone al Monte Somma

After the occurrence described by of Balassone et al. (2001), a second finding of corundum, Al2O3, occurred in a small fragment of carbonatic rock at San Vito quarry, Ercolano, Napoli, Campania. It is the section of a 2 mm bluish crystal. The identification was done through SEM-EDX analysis at 30 kV excitation