A strong-coupling analysis of two-dimensional O(N) sigma models with N≥3N\geq 3 on square, triangular and honeycomb lattices

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ 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 $\beta$ and in the energy $E$. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-$N$ 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 $N$, departing from their large-$N$ values only by a few per mille even down to $N=3$.Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi

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

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

Trap-size scaling in confined particle systems at quantum transitions

We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its quadratic Hamiltonian representation. We discuss trap-size scaling at the Mott insulator to superfluid transition in the Bose-Hubbard model. We present exact and accurate numerical results for the XY chain and for the low-density Mott transition in the hard-core limit of the one-dimensional Bose-Hubbard model. Our results are relevant for systems of cold atomic gases in optical lattices.Comment: Revised and greatly expanded. 15 pages, 7 figure

Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Gauged O(n) spin models in one dimension

We consider a gauged O(n) spin model, n >= 2, in one dimension which contains both the pure O(n) and RP(n-1) models and which interpolates between them. We show that this model is equivalent to the non-interacting sum of the O(n) and Ising models. We derive the mass spectrum that scales in the continuum limit, and demonstrate that there are two universality classes, one of which contains the O(n) and RP(n-1) models and the other which has a tuneable parameter but which is degenerate in the sense that it arises from the direct sum of the O(n) and Ising models.Comment: 9 pages, no figures, LaTeX sourc

More nonperturbative corrections to the fine and hyperfine splitting in the heavy quarkonium

The leading nonperturbative effects to the fine and hyperfine splitting were calculated some time ago. Recently, they have been used in order to obtain realistic numerical results for the lower levels in bottomonium systems. We point out that a contribution of the same order $O(\Lambda_{QCD}^4/m^3 \alpha_s^2)$ has been overlooked. We calculate it in this paper.Comment: 9 pages, LaTeX, More self-contained and lengthier version without changing physical outputs. To be published in Phys. Rev.

Static potential in baryon

The baryon static potential is calculated in the framework of field correlator method and is shown to match the recent lattice results. The effects of the nonzero value of the gluon correlation length are emphasized.Comment: 7 pages, 4 figures, talk at the NPD-2002 Conference, December 2-6, ITEP, Mosco

Coexistence of monopoles and instantons for different topological charge definitions and lattice actions

We compute instanton sizes and study correlation functions between instantons and monopoles in maximum abelian projection within SU(2) lattice QCD at finite temperature. We compare several definitions of the topological charge, different lattice actions and methods of reducing quantum fluctuations. The average instanton size turns out to be $\sigma \approx 0.2$ fm. The correlation length between monopoles and instantons is $\zeta \approx 0.25$ fm and hardly affected by lattice artifacts as dislocations. We visualize several specific gauge field configurations and show directly that there is an enhanced probability for finding monopole loops in the vicinity of instantons. This feature is independent of the topological charge definition used.Comment: 10 pages, LaTeX, uses elsart.sty and elsart12.sty, 16 eps files, 4 figures, published, for corresponding movies (MPEG) see http://www.tuwien.ac.at/e142/Lat/qcd.htm

Application of the varying coefficient model to the behaviour risk factor surveillance data in Italy: a study of changing smoking prevalence among sub-populations

Background: Behaviour risk factor surveillance (BRFS) data can be an important source of information for studying changes in various health outcomes and risk factors. Results obtained from surveillance data analysis are vital for informing health policy interventions, particularly with regards to evolutionary aspects. The objective of this analysis was to recommend a method that can be used for analysing trends in the association among variables from large public health data sets. This was demonstrated by examining the changing effects of various covariates, representing different sub-populations, on smoking status over time. Methods: In our work, we propose the use of varying coefficient models (VCM) with non-parametric techniques to catch the dynamics of the evolutionary processes under study. This is a useful method, which allows coefficients to vary with time using smooth functions. Italian BRFS data from 2008-2012 was used with a sample size of 185,619 observations. In the application, a time VCM is fit for a smoking status binary outcome variable using the P-spline estimation method. The model includes ten independent variables comprising socio-demographic, health risk and behaviour variables. Results: The VCM fit for the data indicates that the coefficients for some of the categories for the age and the alcohol consumption variables varied with time. The main results show that Italians aged 18-29 and 40-49 had higher odds of being smokers compared to those aged 60-69; however, these odds significantly decreased in the period 2008-2012. In addition, those who do not drink had lower odds for being a smoker compared to high risk drinkers and these odds decreased further during the observation period. Conclusion: The application of the VCM to the BRFS data in Italy has shown that this method can be useful in detecting which sub-populations require interventions. Although the results have shown a decrease in the odds of being a smoker for certain age groups and non-drinkers, other sub-populations have not decreased their odds and health inequalities remain. This observation indicates that efforts and interventions are still required to target these non-changing sub-populations in order to modify their smoking behaviour.Background: Behaviour risk factor surveillance (BRFS) data can be an important source of information for studying changes in various health outcomes and risk factors. Results obtained from surveillance data analysis are vital for informing health policy interventions, particularly with regards to evolutionary aspects. The objective of this analysis was to recommend a method that can be used for analysing trends in the association among variables from large public health data sets. This was demonstrated by examining the changing effects of various covariates, representing different sub-populations, on smoking status over time.Methods: In our work, we propose the use of varying coefficient models (VCM) with non-parametric techniques to catch the dynamics of the evolutionary processes under study. This is a useful method, which allows coefficients to vary with time using smooth functions. Italian BRFS data from 2008-2012 was used with a sample size of 185,619 observations. In the application, a time VCM is fit for a smoking status binary outcome variable using the P-spline estimation method. The model includes ten independent variables comprising socio-demographic, health risk and behaviour variables.Results: The VCM fit for the data indicates that the coefficients for some of the categories for the age and the alcohol consumption variables varied with time. The main results show that Italians aged 18-29 and 40-49 had higher odds of being smokers compared to those aged 60-69; however, these odds significantly decreased in the period 2008-2012. In addition, those who do not drink had lower odds for being a smoker compared to high risk drinkers and these odds decreased further during the observation period.Conclusion: The application of the VCM to the BRFS data in Italy has shown that this method can be useful in detecting which sub-populations require interventions. Although the results have shown a decrease in the odds of being a smoker for certain age groups and non-drinkers, other sub-populations have not decreased their odds and health inequalities remain. This observation indicates that efforts and interventions are still required to target these non-changing sub-populations in order to modify their smoking behaviour