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

Eliminating leading corrections to scaling in the 3-dimensional O(N)-symmetric phi^4 model: N=3 and 4

We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size scaling method. We find that there exists a finite value of the coupling lambda^*, for both values of N, where leading corrections to scaling vanish. As a first application, we compute the critical exponents nu=0.710(2) and eta=0.0380(10) for N=3 and nu=0.749(2) and eta=0.0365(10) for N=4.Comment: 21 pages, 2 figure

Infrared Renormalons and Finite Volume

We analyze the perturbative expansion of a condensate in the O(N) non-linear sigma model for large N on a two dimensional finite lattice. On an infinite volume this expansion is affected by an infrared renormalon. We extrapolate this analysis to the case of the gluon condensate of Yang-Mills theory and argue that infrared renormalons can be detected by performing perturbative studies even on relatively small lattices.Comment: LaTeX file, 6 figures in postscrip

The Abelianicity of Cooled SU(2) Lattice Configurations

We introduce a gauge-invariant measure of the local "abelianicity" of any given lattice configuration in non-abelian lattice gauge theory; it is essentially a comparison of the magnitude of field strength commutators to the magnitude of the field strength itself. This measure, in conjunction with the cooling technique, is used to probe the SU(2) lattice vacuum for a possible large-scale abelian background, underlying the local short-range field fluctuations. We do, in fact, find a substantial rise in abelianicity over 10 cooling steps or so, after which the abelianicity tends to drop again.Comment: 10 pages, Latex, uses psfi

Seismic vulnerability assessment on a territorial scale based on a Bayesian approach

Italian historical centres are mostly characterized by aggregate buildings. As defined by the Italian codes (Norme Tecniche per le Costruzioni 2008 and Circolare n. 617), the analysis of the most representative local mechanisms of collapse must be performed in order to assess their vulnerability. In this article, the out-of-plane local mechanisms of collapse analysis is implemented by applying a new method of analysis based on a probabilistic approach. Usually information which are necessary for the implementation of the local mechanisms analyses are affected by uncertainty or are missing, therefore in lots of cases it is only possible to hypothesize them on the basis of the other buildings information collected during the on-site survey. In this context, the implementation of a Bayesian approach allows to deduce buildings lacking information (i.e. wall thickness and interstorey height) starting from certain collected data (i.e. facades height). The historical centre of Timisoara (Romania) is selected as the case study for the implementation of this new method of analysis, given the extension of the on-site survey already carried out in the area (information about more than 200 structural units have been collected) and the seismic vulnerability assessment on an urban scale already performed by applying a traditional method. Results obtained by adopting the two approaches are then compared and a validation and a calibration of the new one is carried out

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

The application of a Bayesian approach to assess the seismic vulnerability of historical centers

The seismic vulnerability of historical centers at a territorial scale cannot be assessed performing detailed analysis which are usually adopted at the single building scale. In fact, a traditional complete survey would be extremely time-consuming and not sustainable for this purpose. The approach described in this paper is based on the idea that it is possible to infer quantities which cannot be directly detected from buildings outside inspection starting from parameters that can be measured. In order to achieve this purpose, a Bayesian approach is applied, updating initial hypotheses when new data become available. In this context, the procedure herein proposed aims at applying a probabilistic approach instead of a deterministic one to define facades inter-storey height starting from buildings height knowledge. In order to validate the method, for out of plane local mechanisms of collapse (walls overturning), horizontal loads multiplier \uf0610 values are calculated and compared to results obtained by using data collected on-site

Critical renormalized coupling constants in the symmetric phase of the Ising models

Using a novel finite size scaling Monte Carlo method, we calculate the four, six and eight point renormalized coupling constants defined at zero momentum in the symmetric phase of the three dimensional Ising system. The results of the 2D Ising system that were directly measured are also reported. Our values of the six and eight point coupling constants are significantly different from those obtained from other methods.Comment: 7 pages, 2 figure

Large-N phase transition in lattice 2-d principal chiral models

We investigate the large-N critical behavior of 2-d lattice chiral models by Monte Carlo simulations of U(N) and SU(N) groups at large N. Numerical results confirm strong coupling analyses, i.e. the existence of a large-N second order phase transition at a finite $\beta_c$.Comment: 12 pages, Revtex, 8 uuencoded postscript figure

The three-dimensional XY universality class: A high precision Monte Carlo estimate of the universal amplitude ratio A_+/A_-

We simulate the improved three-dimensional two-component phi^4 model on the simple cubic lattice in the low and the high temperature phase for reduced temperatures down to |T-T_c|/T_c \approx 0.0017 on lattices of a size up to 350^3. Our new results for the internal energy and the specific heat are combined with the accurate estimates of beta_c and data for the internal energy and the specific heat at \beta_c recently obtained in cond-mat/0605083. We find R_{\alpha} = (1-A_+/A_-)/\alpha = 4.01(5), where alpha is the critical exponent of the specific heat and A_{\pm} is the amplitude of the specific heat in the high and the low temperature phase, respectively.Comment: 14 pages, 4 figure