Strong coupling analysis of the large-N 2-d lattice chiral models

Two dimensional large-N chiral models on the square and honeycomb lattices are investigated by a strong coupling analysis. Strong coupling expansion turns out to be predictive for the evaluation of continuum physical quantities, to the point of showing asymptotic scaling. Indeed in the strong coupling region a quite large range of beta values exists where the fundamental mass agrees, within about 5% on the square lattice and about 10% on the honeycomb lattice, with the continuum predictions in the %%energy scheme.Comment: 16 pages, Revtex, 8 uuencoded postscript figure

The two-point correlation function of three-dimensional O(N) models: critical limit and anisotropy

In three-dimensional O(N) models, we investigate the low-momentum behavior of the two-point Green's function G(x) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotational-invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice non-linear O(N) sigma models, 1/N-expansion, field-theoretical methods within the phi^4 continuum formulation. In non-rotational invariant physical systems with O(N)-invariant interactions, the vanishing of space-anisotropy approaching the rotational-invariant fixed point is described by a critical exponent rho, which is universal and is related to the leading irrelevant operator breaking rotational invariance. At N=\infty one finds rho=2. We show that, for all values of $N\geq 0$, $\rho\simeq 2$. Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small.Comment: 65 pages, revte

A New Technique for Measuring the Strangemess Content of the Proton on the Lattice

A new technique for computing the strangeness content of the proton on the lattice is described. It is applied to the calculation of the strange quark contribution to the proton's spin, specifically to the evaluation of the proton matrix element of the strange quark axial current. Preliminary results are not in disagreement with the EMC experiment. NOTE: This paper is available only in postscript form.Comment: 8 pages, figures included in the text, all in postscrip

Application of the O(N)O(N)-Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional σ\sigma-Models and to the Generation of High-Temperature Expansions in Higher Dimensions

In this talk we present the exact solution of the most general one-dimensional $O(N)$-invariant spin model taking values in the sphere $S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible continuum limits. All these results are obtained using a high-temperature expansion in terms of hyperspherical harmonics. Applications in higher dimensions of the same technique are then discussed.Comment: 59208 bytes uuencoded gzip'ed (expands to 135067 bytes Postscript); 4 pages including all figures; contribution to Lattice '9

A strong-coupling analysis of two-dimensional O(N) sigma models with N≥3N\geq 3 on square, triangular and honeycomb lattices

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ models are analyzed, focusing on the evaluation of dimensionless renormalization-group invariant ratios of physical quantities and applying resummation techniques to series in the inverse temperature $\beta$ and in the energy $E$. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-$N$ solutions are carefully studied in order to establish benchmarks for series coefficients and resummations. Scaling and universality are verified. All invariant ratios related to the large-distance properties of the two-point functions vary monotonically with $N$, departing from their large-$N$ values only by a few per mille even down to $N=3$.Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi

Gauge--invariant field correlators in QCD at finite temperature

We study by numerical simulations on a lattice the behaviour of the gauge--invariant two--point correlation functions of the gauge field strengths across the deconfinement phase transition.Comment: 12 pages, LaTeX file, + 5 PS figures, uuencoded-tar-compresse

Gauge-invariant nonlocal quark condensates in QCD

We study, by numerical simulations on a lattice, the behaviour of the gauge-invariant nonlocal quark condensates in the QCD vacuum both in the quenched approximation and with four flavours of dynamical staggered fermions. The correlation length of the condensate is determined to be roughly twice as big as in the case of the gluon field strength correlators.Comment: LATTICE98(confine

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

On the dependence of the gauge-invariant field-strength correlators in QCD on the shape of the Schwinger string

We study, by numerical simulations on a lattice, the dependence of the gauge-invariant two-point field-strength correlators in QCD on the path used to perform the color parallel transport between the two points.Comment: 9 pages, LaTeX file, + 5 PS figures. Revised version (accepted for publication in Physics Letters B) with new comments on the result

Field strength correlators in QCD at zero and non-zero temperature

We study, by numerical simulations on a lattice, the behaviour of the gauge--invariant field strength correlators in QCD both at zero temperature, down to a distance of 0.1 fm, and at finite temperature, across the deconfinement phase transition.Comment: Talk given at the ``High Energy Conference on Quantum Chromodynamics'', Montpellier (France), 4-12 July 1996 (QCD 96); 5 pages, LaTeX file, uses ``espcrc2.sty''+ 5 PS figure