1,587 research outputs found
Topological susceptibility and string tension in CP(N-1) models
We investigate the features of models concerning confinement
and topology. In order to study the approach to the large- asymptotic
regime, we determine the topological susceptibility and the string tension for
a wide range of values of , in particular . Quantitative
agreement with the large- predictions is found for the and
the models. Problems related to the measure of the topological
susceptibility and the string tension on the lattice are discussed.Comment: Talk presented at the Lattice '92 Conference, Amsterdam. 6 pages,
sorry, no figures included, if required we can send them by mai
Monte Carlo simulation of lattice models at large N
In order to check the validity and the range of applicability of the 1/N
expansion, we performed numerical simulations of the two-dimensional lattice
CP(N-1) models at large N, in particular we considered the CP(20) and the
CP(40) models. Quantitative agreement with the large-N predictions is found for
the correlation length defined by the second moment of the correlation
function, the topological susceptibility and the string tension. On the other
hand, quantities involving the mass gap are still far from the large-
results showing a very slow approach to the asymptotic regime. To overcome the
problems coming from the severe form of critical slowing down observed at large
N in the measurement of the topological susceptibility by using standard local
algorithms, we performed our simulations implementing the Simulated Tempering
method.Comment: 4 page
Topological charge on the lattice: a field theoretical view of the geometrical approach
We construct sequences of ``field theoretical'' (analytical) lattice
topological charge density operators which formally approach geometrical
definitions in 2-d models and 4-d Yang Mills theories. The
analysis of these sequences of operators suggests a new way of looking at the
geometrical method, showing that geometrical charges can be interpreted as
limits of sequences of field theoretical (analytical) operators. In
perturbation theory renormalization effects formally tend to vanish along such
sequences. But, since the perturbative expansion is asymptotic, this does not
necessarily lead to well behaved geometrical limits. It indeed leaves open the
possibility that non-perturbative renormalizations survive.Comment: 14 pages, revte
Equation of state for systems with Goldstone bosons
We discuss some recent determinations of the equation of state for the XY and
the Heisenberg universality class.Comment: 5 pages, Proceedings of the Conference "Horizons in Complex Systems",
Messina; in honor of the 60th birthday of H.E. Stanle
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
Expansion of Two-Dimensional Models in the Scaling Region
The main technical and conceptual features of the lattice expansion in
the scaling region are discussed in the context of a two-parameter
two-dimensional spin model interpolating between and
models, with standard and improved lattice actions. We show how to
perform the asymptotic expansion of effective propagators for small values of
the mass gap and how to employ this result in the evaluation of physical
quantities in the scaling regime. The lattice renormalization group
function is constructed explicitly and exactly to .Comment: 6 pages, report no. IFUP-TH 49/9
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
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
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