871 research outputs found
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 , . 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 on square, triangular and honeycomb lattices
Recently-generated long strong-coupling series for the two-point Green's
functions of asymptotically free lattice 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 and in the energy . Square,
triangular, and honeycomb lattices are considered, as a test of universality
and in order to estimate systematic errors. Large- 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 , departing from their large- values only by a few per
mille even down to .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
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