732 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 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
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
Application of the -Hyperspherical Harmonics to the Study of the Continuum Limits of One-Dimensional -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 -invariant spin model taking values in the sphere
, 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
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
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
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
Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice
We study the quantum (zero-temperature) critical behaviors of confined
particle systems described by the one-dimensional (1D) Bose-Hubbard model in
the presence of a confining potential, at the Mott insulator to superfluid
transitions, and within the gapless superfluid phase. Specifically, we consider
the hard-core limit of the model, which allows us to study the effects of the
confining potential by exact and very accurate numerical results. We analyze
the quantum critical behaviors in the large trap-size limit within the
framework of the trap-size scaling (TSS) theory, which introduces a new trap
exponent theta to describe the dependence on the trap size. This study is
relevant for experiments of confined quasi 1D cold atom systems in optical
lattices. At the low-density Mott transition TSS can be shown analytically
within the spinless fermion representation of the hard-core limit. The
trap-size dependence turns out to be more subtle in the other critical regions,
when the corresponding homogeneous system has a nonzero filling f, showing an
infinite number of level crossings of the lowest states when increasing the
trap size. At the n=1 Mott transition this gives rise to a modulated TSS: the
TSS is still controlled by the trap-size exponent theta, but it gets modulated
by periodic functions of the trap size. Modulations of the asymptotic power-law
behavior is also found in the gapless superfluid region, with additional
multiscaling behaviors.Comment: 26 pages, 34 figure
Topology in 2D CP**(N-1) models on the lattice: a critical comparison of different cooling techniques
Two-dimensional CP**(N-1) models are used to compare the behavior of
different cooling techniques on the lattice. Cooling is one of the most
frequently used tools to study on the lattice the topological properties of the
vacuum of a field theory. We show that different cooling methods behave in an
equivalent way. To see this we apply the cooling methods on classical
instantonic configurations and on configurations of the thermal equilibrium
ensemble. We also calculate the topological susceptibility by using the cooling
technique.Comment: 24 pages, 10 figures (from 16 eps files
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