Aging dynamics of +-J Edwards-Anderson spin glasses

We analyze by means of extensive computer simulations the out of equilibrium dynamics of Edwards-Anderson spin glasses in d=4 and d=6 dimensions with +-J interactions. In particular, we focus our analysis on the scaling properties of the two-time autocorrelation function in a range of temperatures from T=0.07 T_c to T=0.75 T_c in both systems. We observe that the aging dynamics of the +-J models is different from that observed in the corresponding Gaussian models. In both the 4d and 6d models at very low temperatures we study the effects of discretization of energy levels. Strong interrupted aging behaviors are found. We argue that this is because in the times accessible to our simulations the systems are only able to probe activated dynamics through the lowest discrete energy levels and remain trapped around nearly flat regions of the energy landscape. For temperatures T >= 0.5 T_c in 4d we find logarithmic scalings that are compatible with dynamical ultrametricity, while in 6d the relaxation can also be described by super-aging scalings.Comment: 7 pages, 10 figure

Distribution of Eigenvalues of Ensembles of Asymmetrically Diluted Hopfield Matrices

Using Grassmann variables and an analogy with two dimensional electrostatics, we obtain the average eigenvalue distribution $\rho(\omega)$ of ensembles of $N \times N$ asymmetrically diluted Hopfield matrices in the limit $N \rightarrow \infty$. We found that in the limit of strong dilution the distribution is uniform in a circle in the complex plane.Comment: 9 pages, latex, 4 figure

Canonical solution of a system of long-range interacting rotators on a lattice

The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees' Comments it has been transferred to Phys. Rev. E, because of supposed no general interest. Divided into sections, corrections in (5) and (20), reference 5 updated. 8 pages 1 figur

Trade openness and income: A tale of two regions

In this article we present evidence of the long-run effect of trade openness on income per worker for two regions that have followed different liberalization strategies, namely Asia and Latin America. A model that re-examines these questions is estimated for two panels of Asian and Latin American countries over the 1980-2008 period using a novel empirical approach that accounts for endogeneity as well as for the time series properties of the variables involved. From an econometric point of view, we apply recent panel cointegration techniques based on factor models that account for two additional elements usually neglected in previous empirical literature: cross-dependence and structural breaks. The results point to a positive impact of trade openness in both Asia and Latin America although the size is smaller in the second region. We associate this finding with the degree to which trade was managed in both regions of the developing world

Trade Openness and Income: A Tale of Two Regions

In this article we present evidence of the long-run effect of trade openness on income per worker for two regions that have followed different liberalization strategies, namely Asia and Latin America. A model that re-examines these questions is estimated for two panels of Asian and Latin American countries over the 1980-2008 period using a novel empirical approach that accounts for endogeneity as well as for the time series properties of the variables involved. From an econometric point of view, we apply recent panel cointegration techniques based on factor models that account for two additional elements usually neglected in previous empirical literature: cross-dependence and structural breaks. The results point to a positive impact of trade openness in both Asia and Latin America although the size is smaller in the second region. We associate this finding with the degree to which trade was managed in both regions of the developing world.Spanish Ministry of Education mobility programme (Grant ref. PRX12/00103) The authors also acknowledge the funding from Spanish MINECO (project ECO2014-58991-C3-2-R), Generalitat Valenciana (project PROMETEOII/2014/053), University Jaume I (project P1-1B2013-06) and the European Commission (Lifelong Learning Program- references 542457-LLP-1-2013-1-ES-AJM-CL (M. Camarero), 542434-LLP-1-2013-1-ES-AJM-CL (C. Tamarit) and 542727-LLP-1-2013-1-ES-AJM-C

The U(1)A anomaly in noncommutative SU(N) theories

We work out the one-loop $U(1)_A$ anomaly for noncommutative SU(N) gauge theories up to second order in the noncommutative parameter $\theta^{\mu\nu}$. We set $\theta^{0i}=0$ and conclude that there is no breaking of the classical $U(1)_A$ symmetry of the theory coming from the contributions that are either linear or quadratic in $\theta^{\mu\nu}$. Of course, the ordinary anomalous contributions will be still with us. We also show that the one-loop conservation of the nonsinglet currents holds at least up to second order in $\theta^{\mu\nu}$. We adapt our results to noncommutative gauge theories with SO(N) and U(1) gauge groups.Comment: 50 pages, 5 figures in eps files. Some comments and references adde

Fitting in a complex chi^2 landscape using an optimized hypersurface sampling

Fitting a data set with a parametrized model can be seen geometrically as finding the global minimum of the chi^2 hypersurface, depending on a set of parameters {P_i}. This is usually done using the Levenberg-Marquardt algorithm. The main drawback of this algorithm is that despite of its fast convergence, it can get stuck if the parameters are not initialized close to the final solution. We propose a modification of the Metropolis algorithm introducing a parameter step tuning that optimizes the sampling of parameter space. The ability of the parameter tuning algorithm together with simulated annealing to find the global chi^2 hypersurface minimum, jumping across chi^2{P_i} barriers when necessary, is demonstrated with synthetic functions and with real data

Directed Molecular Stacking for Engineered Fluorescent Three-Dimensional Reduced Graphene Oxide and Coronene Frameworks

[EN] Three‐dimensional fluorescent graphene frameworks with controlled porous morphologies are of significant importance for practical applications reliant on controlled structural and electronic properties, such as organic electronics and photochemistry. Here we report a synthetically accessible approach concerning directed aromatic stacking interactions to give rise to new fluorogenic 3D frameworks with tuneable porosities achieved through molecular variations. The binding interactions between the graphene‐like domains present in the in situ‐formed reduced graphene oxide (rGO) with functional porphyrin molecules lead to new hybrids via an unprecedented solvothermal reaction. Functional free‐base porphyrins featuring perfluorinated aryl groups or hexyl chains at their meso‐ and β‐positions were employed in turn to act as directing entities for the assembly of new graphene‐based and foam‐like frameworks and of their corresponding coronene‐based hybrids. Investigations in the dispersed phase and in thin‐film by XPS, SEM and FLIM shed light onto the nature of the aromatic stacking within functional rGO frameworks (denoted rGOFs) which was then modelled semi‐empirically and by DFT calculations. The pore sizes of the new emerging reduced graphene oxide hybrids are tuneable at the molecular level and mediated by the bonding forces with the functional porphyrins acting as the “molecular glue”. Single crystal X‐ray crystallography described the stacking of a perfluorinated porphyrin with coronene, which can be employed as a molecular model for understanding the local aromatic stacking order and charge transfer interactions within these rGOFs for the first time. This opens up a new route to controllable 3D framework morphologies and pore size from the Ångstrom to the micrometre scale. Theoretical modelling showed that the porosity of these materials is mainly due to the controlled inter‐planar distance between the rGO, coronene or graphene sheets. The host‐guest chemistry involves the porphyrins acting as guests held through π‐π stacking, as demonstrated by XPS. The objective of this study is also to shed light into the fundamental localised electronic and energy transfer properties in these new molecularly engineered porous and fluorogenic architectures, aiming in turn to understand how functional porphyrins may exert stacking control over the notoriously disordered local structure present in porous reduced graphene oxide fragments. By tuning the porosity and the distance between the graphene sheets using aromatic stacking with porphyrins, it is also possible to tune the electronic structure of the final nanohybrid material, as indicated by FLIM experiments on thin films. Such nanohybrids with highly controlled pores dimensions and morphologies open the way to new design and assembly of storage devices and applications incorporating π‐conjugated molecules and materials and their π‐stacks may be relevant towards selective separation membranes, water purification and biosensing applications.S.I.P. and S.W.B. thank The Royal Society and STFC for funding. B.Y.M. thanks the University of Bath for a studentship (ORS). D.G.C. thanks the Fundación General CSIC for funding (ComFuturo Program). Dr. Jose A. Ribeiro Martins, Professors Jeremy K. M. Sanders and Paul Raithby are acknowledged for training, helpful discussions and porphyrin supramolecular chemistry. The S.I.P. group thanks the EPSRC for funding to the Centre of Graphene Science (EP/K017160/1) and to the Centre for Doctoral Training in Sustainable Chemical Technologies (EP/L016354/1). The authors thank EPSRC National Service for Mass Spectrometry at Swansea and EPSRC National Service for Crystallography at Southampton for data collection. The authors also acknowledge the ERC for the Consolidator Grant O2SENSE (617107, 2014–2019)

Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices

For commutative Euclidean time, we study the existence of field configurations that {\it a)} are formal power series expansions in h\theta^{\m\n}, {\it b)} go to ordinary (anti-)instantons as h\theta^{\m\n}\to 0, and {\it c)} render stationary the classical action of Euclidean noncommutative SU(3) Yang-Mills theory. We show that the noncommutative (anti-)self-duality equations have no solutions of this type at any order in h\theta^{\m\n}. However, we obtain all the deformations --called first-order-in-$\theta$-deformed instantons-- of the ordinary instanton that, at first order in h\theta^{\m\n}, satisfy the equations of motion of Euclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantum effects that these field configurations give rise to in noncommutative SU(3) with one, two and three nearly massless flavours and compute the corresponding 't Hooft vertices, also, at first order in h\theta^{\m\n}. Other issues analyzed in this paper are the existence at higher orders in h\theta^{\m\n} of topologically nontrivial solutions of the type mentioned above and the classification of the classical vacua of noncommutative SU(N) Yang-Mills theory that are power series in h\theta^{\m\n}.Comment: Latex. Some macros. No figures. 42 pages. Typos correcte