Three-Loop Results on the Lattice

We present some new three-loop results in lattice gauge theories, for the Free Energy and for the Topological Susceptibility. These results are an outcome of a scheme which we are developing (using a symbolic manipulation language), for the analytic computation of renormalization functions on the lattice.Comment: (Contribution to Lattice-92 conference). 4 page

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

The Three-Loop Lattice Free Energy

We calculate the free energy of SU(N) gauge theories on the lattice, to three loops. Our result, combined with Monte Carlo data for the average plaquette, gives a more precise estimate of the gluonic condensate.Comment: 5 pages + 2 figures (PostScript); report no. IFUP-TH 17/9

Topology in CP(N-1) models: a critical comparison of different cooling techniques

Various cooling methods, including a recently introduced one which smoothes out only quantum fluctuations larger than a given threshold, are applied to the study of topology in 2d CP(N-1) models. A critical comparison of their properties is performed.Comment: Poster at LATTICE99(Topology and confinement), 3 pages, 5 eps figures, uses espcrc2.st

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

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

Quantum Stability of the Phase Transition in Rigid QED

Rigid QED is a renormalizable generalization of Feynman's space-time action characterized by the addition of the curvature of the world line (rigidity). We have recently shown that a phase transition occurs in the leading approximation of the large N limit. The disordered phase essentially coincides with ordinary QED, while the ordered phase is a new theory. We have further shown that both phases of the quantum theory are free of ghosts and tachyons. In this letter, we study the first sub-leading quantum corrections leading to the renormalized mass gap equation. Our main result is that the phase transition does indeed survive these quantum fluctuations.Comment: PHYZZX, 9 pages, 3 Postscript figures, to be published in Nucl. Phys.

Lattice Perturbation Theory by Computer Algebra: A Three-Loop Result for the Topological Susceptibility

We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.Comment: 15 pages + 2 figures (PostScript), report no. IFUP-TH 31/9

Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4

We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size scaling method. We find that there exists a finite value of the coupling lambda^*, for both values of N, where leading corrections to scaling vanish. As a first application, we compute the critical exponents nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for N=4.Comment: 21 pages, 2 figure

Renormalization and topological susceptibility on the lattice: SU(2) Yang-Mills theory

The renormalization functions involved in the determination of the topological susceptibility in the SU(2) lattice gauge theory are extracted by direct measurements, without relying on perturbation theory. The determination exploits the phenomenon of critical slowing down to allow the separation of perturbative and non-perturbative effects. The results are in good agreement with perturbative computations.Comment: 12 pages + 4 figures (PostScript); report no. IFUP-TH 10/9