1,703 research outputs found
Randomly dilute spin models: a six-loop field-theoretic study
We consider the Ginzburg-Landau MN-model that describes M N-vector cubic
models with O(M)-symmetric couplings. We compute the renormalization-group
functions to six-loop order in d=3. We focus on the limit N -> 0 which
describes the critical behaviour of an M-vector model in the presence of weak
quenched disorder. We perform a detailed analysis of the perturbative series
for the random Ising model (M=1). We obtain for the critical exponents: gamma =
1.330(17), nu = 0.678(10), eta = 0.030(3), alpha=-0.034(30), beta = 0.349(5),
omega = 0.25(10). For M > 1 we show that the O(M) fixed point is stable, in
agreement with general non-perturbative arguments, and that no random fixed
point exists.Comment: 29 pages, RevTe
Mean-field expansion for spin models with medium-range interactions
We study the critical crossover between the Gaussian and the Wilson-Fisher
fixed point for general O(N)-invariant spin models with medium-range
interactions. We perform a systematic expansion around the mean-field solution,
obtaining the universal crossover curves and their leading corrections. In
particular we show that, in three dimensions, the leading correction scales as
being the range of the interactions. We compare our results with
the existing numerical ones obtained by Monte Carlo simulations and present a
critical discussion of other approaches.Comment: 49 pages, 8 figure
Critical behavior of vector models with cubic symmetry
We report on some results concerning the effects of cubic anisotropy and
quenched uncorrelated impurities on multicomponent spin models. The analysis of
the six-loop three-dimensional series provides an accurate description of the
renormalization-group flow.Comment: 6 pages. Talk given at the V International Conference Renormalization
Group 2002, Strba, Slovakia, March 10-16 200
Nonanalyticity of the beta-function and systematic errors in field-theoretic calculations of critical quantities
We consider the fixed-dimension perturbative expansion. We discuss the
nonanalyticity of the renormalization-group functions at the fixed point and
its consequences for the numerical determination of critical quantities.Comment: 9 page
Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
We study the universal critical behavior of two-dimensional (2D) lattice
bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which
separates the low-temperature superfluid phase from the high-temperature normal
phase. For this purpose, we perform quantum Monte Carlo simulations of the
hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the
critical temperature by using a matching method that relates finite-size data
for the BH model with corresponding data computed in the classical XY model. In
this approach, the neglected scaling corrections decay as inverse powers of the
lattice size L, and not as powers of 1/lnL, as in more standard approaches,
making the estimate of the critical temperature much more reliable. Then, we
consider the BH model in the presence of a trapping harmonic potential, and
verify the universality of the trap-size dependence at the BKT critical point.
This issue is relevant for experiments with quasi-2D trapped cold atoms.Comment: 17 pages, 12 figs, final versio
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
Photoconductance of a one-dimensional quantum dot
The ac-transport properties of a one-dimensional quantum dot with non-Fermi
liquid correlations are investigated. It is found that the linear
photoconductance is drastically influenced by the interaction. Temperature and
voltage dependences of the sideband peaks are treated in detail. Characteristic
Luttinger liquid power laws are founded.Comment: accepted in European Physical Journal
Non-linear analysis of geomagnetic time series from Etna volcano
International audienceAn intensive nonlinear analysis of geomagnetic time series from the magnetic network on Etna volcano was carried out to investigate the dynamical behavior of magnetic anomalies in volcanic areas. The short-term predictability of the geomagnetic time series was evaluated to establish a possible low-dimensional deterministic dynamics. We estimated the predictive ability of both a nonlinear forecasting technique and a global autoregressive model by comparing the prediction errors. Our findings highlight that volcanomagnetic signals are the result of complex processes that cannot easily be predicted. There is slight evidence based on nonlinear predictions, that the geomagnetic time series are to be governed by many variables, whose time evolution could be better regarded as arising from complex high dimensional processes
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