129 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
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
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
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
Universal quantum behaviors of interacting fermions in 1D traps: from few particles to the trap thermodynamic limit
We investigate the ground-state properties of trapped fermion systems
described by the Hubbard model with an external confining potential. We discuss
the universal behaviors of systems in different regimes: from few particles,
i.e. in dilute regime, to the trap thermodynamic limit.
The asymptotic trap-size (TS) dependence in the dilute regime (increasing the
trap size l keeping the particle number N fixed) is described by a universal TS
scaling controlled by the dilute fixed point associated with the
metal-to-vacuum quantum transition. This scaling behavior is numerically
checked by DMRG simulations of the one-dimensional (1D) Hubbard model. In
particular, the particle density and its correlations show crossovers among
different regimes: for strongly repulsive interactions they approach those of a
spinless Fermi gas, for weak interactions those of a free Fermi gas, and for
strongly attractive interactions they match those of a gas of hard-core bosonic
molecules.
The large-N behavior of systems at fixed N/l corresponds to a 1D trap
thermodynamic limit. We address issues related to the accuracy of the local
density approximation (LDA). We show that the particle density approaches its
LDA in the large-l limit. When the trapped system is in the metallic phase,
corrections at finite l are O(l^{-1}) and oscillating around the center of the
trap. They become significantly larger at the boundary of the fermion cloud,
where they get suppressed as O(l^{-1/3}) only. This anomalous behavior arises
from the nontrivial scaling at the metal-to-vacuum transition occurring at the
boundaries of the fermion cloud.Comment: 20 page
Adaptive Optimization of Wave Functions for Lattice Field Models
The accuracy of Green Function Monte Carlo (GFMC) simulations can be greatly
improved by a clever choice of the approximate ground state wave function that
controls configuration sampling. This trial wave function typically depends on
many free parameters whose fixing is a non trivial task. Here, we discuss a
general purpose adaptive algorithm for their non-linear optimization. As a non
trivial application we test the method on the two dimensional Wess-Zumino
model, a relativistically invariant supersymmetric field theory with
interacting bosonic and fermionic degrees of freedom.Comment: 12 pages, 5 EPS figures, Contribution to the Proceedings of the
"Quantum Monte Carlo" meeting (Trento, Italy, July 3-6, 2001
On the evaluation of the improvement parameter in the lattice Hamiltonian approach to critical phenomena
In lattice Hamiltonian systems with a quartic coupling , a critical
value may exist such that, when , the leading
irrelevant operator decouples from the Hamiltonian and the leading nonscaling
contribution to renormalization-group invariant physical quantities (evaluated
in the critical region) vanishes. The 1/N expansion technique is applied to the
evaluation of for the lattice Hamiltonian of vector spin models with
O(N) symmetry. As a byproduct, systematic asymptotic expansions for the
relevant lattice massive one-loop integrals are obtained.Comment: Conclusions clarified; 26 pages, 6 figures, RevTeX
Quantum transitions driven by one-bond defects in quantum Ising rings
We investigate quantum scaling phenomena driven by lower-dimensional defects
in quantum Ising-like models. We consider quantum Ising rings in the presence
of a bond defect. In the ordered phase, the system undergoes a quantum
transition driven by the bond defect between a magnet phase, in which the gap
decreases exponentially with increasing size, and a kink phase, in which the
gap decreases instead with a power of the size. Close to the transition, the
system shows a universal scaling behavior, which we characterize by computing,
either analytically or numerically, scaling functions for the gap, the
susceptibility, and the two-point correlation function. We discuss the
implications of these results for the nonequilibrium dynamics in the presence
of a slowly-varying parallel magnetic field h, when going across the
first-order quantum transition at h=0.Comment: 5 page
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