The influence of long-range hopping on ferromagnetism in the Hubbard model

The phase diagram of the Hubbard model in an external magnetic field is examined by extrapolation of small-cluster exact-diagonalization calculations. Using a general expression for the hopping matrix elements ($t_{ij}\sim q^{|i-j|}$) the influence of long-range hopping (band asymmetry) on ferromagnetism in this model is studied. It is found that the long-range hopping (nonzero $q$) stabilizes ferromagnetism in an external magnetic field for $n > 1$. In the opposite limit $n \leq 1$ the fully polarized ferromagnetic state is generally suppressed with increasing $q$. The critical value of magnetic field $h$ below which the ferromagnetic state becomes unstable is calculated numerically.Comment: 8 pages, 3 Postscript figures, Late

Lateral periodontal cyst: An unusual case report / Cisto periodontal lateral: Relato de caso incomum

Introduction: Lateral periodontal cysts are odontogenic cysts with very unusual development. According to the literature, they account for less than 0.4% of cases of odontogenic cysts. Presentation of Case: The present report describes a 34-year-old patient referred to the maxillofacial surgery and traumatology department of Montenegro Hospital due to swelling of the face with asymptomatic evolution for approximately 1 year. Based on clinical and tomographic examinations, the diagnostic hypothesis was odontogenic cyst, and the surgical plan involved complete enucleation of the cystic lesion. Complete removal was performed, and the material removed was sent for histopathological analysis. The examination revealed an irregular cystic cavity covered by epithelial tissue with few cuboidal layers that showed clear cells in the basal layer in some areas and the formation of nodular epithelial structures that protruded into the cavity. Discussion: The histopathological characteristics described in the literature are consistent with the histopathological description of the enucleated cyst in this case, confirming the diagnosis of lateral periodontal cyst. Conclusion: The patient is currently under follow-up, and evaluations have been normal

Spin Models on Thin Graphs

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional gravity. We highlight the similarity with Bethe lattice calculations and the advantages of the thin graph approach both analytically and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy compressed ps file replaced with uuencoded LaTex original + ps figure

Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists

We review critically the concepts and the applications of Cayley Trees and Bethe Lattices in statistical mechanics in a tentative effort to remove widespread misuse of these simple, but yet important - and different - ideal graphs. We illustrate, in particular, two rigorous techniques to deal with Bethe Lattices, based respectively on self-similarity and on the Kolmogorov consistency theorem, linking the latter with the Cavity and Belief Propagation methods, more known to the physics community.Comment: 10 pages, 2 figure

Optical and magneto-optical response of a doped Mott insulator

We study the optical, Raman, and ac Hall response of the doped Mott insulator within the dynamical mean-field theory (d = infinity ) for strongly correlated electron systems. The occurrence of the isosbectic point in the optical conductivity is shown to be associated with the frequency dependence of the generalized charge susceptibility. We compute the Raman response, which probes the fluctuations of the "stress tensor," and show that the scattering is characterized by appreciable incoherent contributions. The calculated ac Hall constant and Hall angle also exhibit the isosbectic points. These results are also compared with those obtained for a non-FL metal in d = infinity. The role of low-energy coherence (FL) or incoherence (non-FL) in determining the finite frequency response of strongly correlated metals in d = infinity is discussed in detail. As an application of interest, we compute the dielectric figure-of-merit (DFOM), a quantity that is of potential importance for microwave device applications. We demonstrate explicitly that systems near the filling driven Mott transition might be good candidates in this respect, and discuss the influence of real-life factors on the DFOM.64

Fully Frustrated Ising System on a 3D Simple Cubic Lattice: Revisited

Using extensive Monte Carlo simulations, we clarify the critical behaviour of the 3 dimensional simple cubic Ising Fully Frustrated system. We find two transition temperatures and two long range ordered phases. Within the present numerical accuracy, the transition at higher temperature is found to be second order and we have extracted the standard critical exponent using finite size scaling method. On the other hand, the transition at lower temperature is found to be first order. It is argued that entropy plays a major role on determining the low temperature state.Comment: 14 pages 14 figures iop style include

Neuromorphic Hardware In The Loop: Training a Deep Spiking Network on the BrainScaleS Wafer-Scale System

Emulating spiking neural networks on analog neuromorphic hardware offers several advantages over simulating them on conventional computers, particularly in terms of speed and energy consumption. However, this usually comes at the cost of reduced control over the dynamics of the emulated networks. In this paper, we demonstrate how iterative training of a hardware-emulated network can compensate for anomalies induced by the analog substrate. We first convert a deep neural network trained in software to a spiking network on the BrainScaleS wafer-scale neuromorphic system, thereby enabling an acceleration factor of 10 000 compared to the biological time domain. This mapping is followed by the in-the-loop training, where in each training step, the network activity is first recorded in hardware and then used to compute the parameter updates in software via backpropagation. An essential finding is that the parameter updates do not have to be precise, but only need to approximately follow the correct gradient, which simplifies the computation of updates. Using this approach, after only several tens of iterations, the spiking network shows an accuracy close to the ideal software-emulated prototype. The presented techniques show that deep spiking networks emulated on analog neuromorphic devices can attain good computational performance despite the inherent variations of the analog substrate.Comment: 8 pages, 10 figures, submitted to IJCNN 201

Origin of the high sensitivity of Chinese red clay soils to drought: significance of the clay characteristics

International audienceThe red clay soils which are widespread in China are known to be highly sensitive to drought during the dry season but the origin of this high sensitivity to drought remains unclear. Several red clay soils were selected in the Hunan province for study. We studied their basic physico-chemical properties and clay mineralogy, their structure and shrinkage properties, as well as their water retention properties. Results show that the amount of water available between -330 and -15 000 hPa water potential is consistent with that recorded in many other clay soils from different parts of the world and thus cannot explain the high sensitivity of the red clay soils to drought. This high sensitivity to drought might be related to the high proportion of poorly available water which was characterized by the amount of available water between -3300 and -15 000 hPa water potential. Comparison with clay soils located in different parts of the world and for which the sensitivity to drought was not identified, showed that this proportion of poorly available water is indeed much higher in the red clay soils studied than in clay soils representing a large range of both clay content and mineralogy. This specific behaviour of the red clay soils studied is thought to be related to the history of their parent materials: these materials are continental sediments which may have been submitted to great hydric stress, thus leading to strongly consolidated soils with consequences such as a high proportion of poorly available water, strong aggregation and weak shrinkage properties

Temperature-dependent electronic structure and ferromagnetism in the d=oo Hubbard model studied by a modfied perturbation theory

The infinite-dimensional Hubbard model is studied by means of a modified perturbation theory. The approach reduces to the iterative perturbation theory for weak coupling. It is exact in the atomic limit and correctly reproduces the dispersions and the weights of the Hubbard bands in the strong-coupling regime for arbitrary fillings. Results are presented for the hyper-cubic and an fcc-type lattice. For the latter we find ferromagnetic solutions. The filling-dependent Curie temperature is compared with the results of a recent Quantum Monte Carlo study.Comment: RevTeX, 5 pages, 6 eps figures included, Phys. Rev. B (in press), Ref. 16 correcte

Yang-Lee and Fisher Zeros of Multisite Interaction Ising Models on the Cayley-type Lattices

A general analytical formula for recurrence relations of multisite interaction Ising models in an external magnetic field on the Cayley-type lattices is derived. Using the theory of complex analytical dynamics on the Riemann sphere, a numerical algorithm to obtain Yang-Lee and Fisher zeros of the models is developed. It is shown that the sets of Yang-Lee and Fisher zeros are almost always fractals, that could be associated with Mandelbrot-like sets on the complex magnetic field and temperature planes respectively.Comment: 9 pages, 3 figures; with minor correction