1,858 research outputs found
On the evaluation of universal non-perturbative constants in O(N) sigma models
We investigate the relation between on-shell and zero-momentum
non-perturbative quantities entering the parametrization of the two-point
Green's function of two-dimensional non-linear O(N) sigma models. We present
accurate estimates of ratios of mass-scales and renormalization constants,
obtained by an analysis of the strong-coupling expansion of the two-point
Green's function. These ratios allow to connect exact known on-shell results
with typical zero-momentum lattice evaluations. Our results are supported by
the 1/N-expansion.Comment: 10 pages, revte
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
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
Critical behavior of the correlation function of three-dimensional O(N) models in the symmetric phase
We present new strong-coupling series for O(N) spin models in three
dimensions, on the cubic and diamond lattices. We analyze these series to
investigate the two-point Green's function G(x) in the critical region of the
symmetric phase. This analysis shows that the low-momentum behavior of G(x) is
essentially Gaussian for all N from zero to infinity. This result is also
supported by a large-N analysis.Comment: 3 pages, requires espcrc2.st
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
Scaling and asymptotic scaling in two-dimensional models
Two-dimensional models are investigated by Monte Carlo methods on
the lattice, for values of ranging from 2 to 21. Scaling and rotation
invariance are studied by comparing different definitions of correlation length
. Several lattice formulations are compared and shown to enjoy scaling for
as small as . Asymptotic scaling is investigated using as bare
coupling constant both the usual and (related to the internal
energy); the latter is shown to improve asymptotic scaling properties. Studies
of finite size effects show their -dependence to be highly non-trivial, due
to the increasing radius of the bound states at large .Comment: 5 pages + 12 figures (PostScript), report no. IFUP-TH 46/9
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
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