Nature of the Spin-glass State in the Three-dimensional Gauge Glass

We present results from simulations of the gauge glass model in three dimensions using the parallel tempering Monte Carlo technique. Critical fluctuations should not affect the data since we equilibrate down to low temperatures, for moderate sizes. Our results are qualitatively consistent with earlier work on the three and four dimensional Edwards-Anderson Ising spin glass. We find that large scale excitations cost only a finite amount of energy in the thermodynamic limit, and that those excitations have a surface whose fractal dimension is less than the space dimension, consistent with a scenario proposed by Krzakala and Martin, and Palassini and Young.Comment: 5 pages, 7 figure

The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking

We present a general and powerful numerical method useful to study the density matrix of spin models. We apply the method to finite dimensional spin glasses, and we analyze in detail the four dimensional Edwards-Anderson model with Gaussian quenched random couplings. Our results clearly support the existence of replica symmetry breaking in the thermodynamical limit.Comment: 8 pages, 13 postscript figure

Monte Carlo simulations of the four-dimensional XY spin glass at low temperatures

We report results for simulations of the four-dimensional XY spin glass using the parallel tempering Monte Carlo method at low temperatures for moderate sizes. Our results are qualitatively consistent with earlier work on the three-dimensional gauge glass as well as three- and four-dimensional Edwards-Anderson Ising spin glass. An extrapolation of our results would indicate that large-scale excitations cost only a finite amount of energy in the thermodynamic limit. The surface of these excitations may be fractal, although we cannot rule out a scenario compatible with replica symmetry breaking in which the surface of low-energy large-scale excitations is space filling.Comment: 6 pages, 8 figure

Remarks on the determination of the Landau gauge OPE for the Asymmetric three gluon vertex

We compute a compact OPE formula describing power corrections to the perturbative expression for the asymmetric $\widetilde{MOM}$-renormalized running coupling constant up to the leading logarithm. By the use of the phenomelogical hypothesis leading to the factorization of the condensates through a perturbative vacuum insertion, the only relevant condensate in the game is $$. The validity of the OPE formula is tested by searching for a good-quality coherent description of previous lattice evaluations of $\widetilde{MOM}$-renormalized gluon propagator and running coupling.Comment: 12 pages, 3 figures (2 generated by the macro: axodraw.sty

Glassy Vortex State in a Two-Dimensional Disordered XY-Model

The two-dimensional XY-model with random phase-shifts on bonds is studied. The analysis is based on a renormalization group for the replicated system. The model is shown to have an ordered phase with quasi long-range order. This ordered phase consists of a glass-like region at lower temperatures and of a non-glassy region at higher temperatures. The transition from the disordered phase into the ordered phase is not reentrant and is of a new universality class at zero temperature. In contrast to previous approaches the disorder strength is found to be renormalized to larger values. Several correlation functions are calculated for the ordered phase. They allow to identify not only the transition into the glassy phase but also an additional crossover line, where the disconnected vortex correlation changes its behavior on large scales non-analytically. The renormalization group approach yields the glassy features without a breaking of replica symmetry.Comment: latex 12 pages with 3 figures, using epsf.sty and multicol.st

Seismic Vulnerability of Heritage Churches in Québec: the Néo-Roman Typology

Several seismic events have demonstrated the vulnerability of masonry churches. The long seismic history of the Italian territory has provided materials to observe and to study the structural performance of churches. Since the 1976 Friuli earthquake many studies have contributed to the definition of specific damage and vulnerability assessment methods for churches, based on the identification of macro-elements and kinematic mechanisms. In this context, the paper presents the application of a vulnerability assessment methodology developed and currently applied in Italy to a case study representative of the néo-roman church typology in Montreal, Québec. The study is part of a collaborative project between Politecnico di Milano and École de Technologie Supérieure of Montreal. The relevance of such a study derives from the moderate seismicity of Montreal associated to a high density of churches. Starting from a previous inventory of 108 churches in Montreal Island, the Néo-roman church typology was selected to be investigated. Specificities of this typology are the position of the bell tower in the middle of the façade and the interaction between the timber structure and masonry walls. This combination between the façade and bell tower macro-elements requires to reconsider the mechanisms associated to these elements in the original reference method. A detailed survey of the roof and bell tower timber structures of a néo-roman church was done, and a three-dimensional numerical model was developed for a better understanding of this type of structure. Modal analysis of a global model was then carried out and the first results of the modal shapes discussed

Ultrametricity in 3D Edwards-Anderson spin glasses

We perform an accurate test of Ultrametricity in the aging dynamics of the three dimensional Edwards-Anderson spin glass. Our method consists in considering the evolution in parallel of two identical systems constrained to have fixed overlap. This turns out to be a particularly efficient way to study the geometrical relations between configurations at distant large times. Our findings strongly hint towards dynamical ultrametricity in spin glasses, while this is absent in simpler aging systems with domain growth dynamics. A recently developed theory of linear response in glassy systems allows to infer that dynamical ultrametricity implies the same property at the level of equilibrium states.Comment: 4 pages, 5 figure

Nonperturbative Effects from the Resummation of Perturbation Theory

Using the general argument in Borel resummation of perturbation theory that links the divergent perturbation theory to the nonperturbative effect we argue that the nonperturbative effect associated with the perturbation theory should have a branch cut only along the positive real axis in the complex coupling plane. The component in the weak coupling expansion of the nonperturbative amplitude, which usually includes the leading term in the weak coupling expansion, that gives rise to the branch cut can be calculated in principle from the perturbation theory combined with some exactly calculable properties of the nonperturbative effect. The realization of this mechanism is demonstrated in the double well potential and the two-dimensional O(N) nonlinear sigma model. In these models the leading term in weak coupling of the nonperturbative effect can be obtained with good accuracy from the first terms of the perturbation theory. Applying this mechanism to the infrared renormalon induced nonperturbative effect in QCD, we suggest some of the QCD condensate effects can be calculated in principle from the perturbation theory.Comment: 21 Pages, 1 Figure; To appear in Phys Rev

Seismic Damage Mechanisms for Churches and Damage Sequence: Considerations from a Case Study

Several high-intensity earthquakes have occurred in Italy in the last decades, causing considerable damage to architectural heritage and pointing out the particularly high seismic vulnerability of masonry churches. A significant research effort has been devoted to develop specific methods for the damage analysis and the seismic vulnerability assessment of these assets. An abacus of damage mechanisms recurring in the church structural components has been developed and has become an important reference in rapid assessment procedures as well as in more detailed analyses. In this perspective, the damage occurred to a church during the Pianura Padana Emiliana (Emilia) Earthquake of 2012 is analyzed here. The damage pattern reproduced, indeed, situations listed in the abacus of mechanisms. The seismic response of the church has been analyzed with different numerical approaches, with complete and with partial models that have allowed an appreciable understanding of the global behavior and of the modality of damage progressing into the mechanisms. The use of vector graphics software tools for 3D modelling that have become available in recent times has allowed to thoroughly understand the constructional complexity of the asset and, consequently, to develop simpler but structurally significant models for numerical analysis

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.Comment: 11 pages, 11 figure