Antiferromagnetic O(N) models in four dimensions

We study the antiferromagnetic O(N) model in the F_4 lattice. Monte Carlo simulations are applied for investigating the behavior of the transition for N=2,3. The numerical results show a first order nature but with a large correlation length. The $N \to \infty$ limit is also considered with analytical methods.Comment: 14 pages, 3 postscript figure

Computer simulation of fatigue under diametrical compression

We study the fatigue fracture of disordered materials by means of computer simulations of a discrete element model. We extend a two-dimensional fracture model to capture the microscopic mechanisms relevant for fatigue, and we simulate the diametric compression of a disc shape specimen under a constant external force. The model allows to follow the development of the fracture process on the macro- and micro-level varying the relative influence of the mechanisms of damage accumulation over the load history and healing of microcracks. As a specific example we consider recent experimental results on the fatigue fracture of asphalt. Our numerical simulations show that for intermediate applied loads the lifetime of the specimen presents a power law behavior. Under the effect of healing, more prominent for small loads compared to the tensile strength of the material, the lifetime of the sample increases and a fatigue limit emerges below which no macroscopic failure occurs. The numerical results are in a good qualitative agreement with the experimental findings.Comment: 7 pages, 8 figures, RevTex forma

Singular diffusion and criticality in a confined sandpile

We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to derive a continuum nonlinear diffusion equation that displays singularities in both the diffusion and drift terms. The stationary-state solutions of this equation, which maximizes the Fermi-Dirac entropy, are in perfect agreement with the spatial profiles of time-averaged occupancy obtained from model numerical simulations in one as well as in two dimensions. Surprisingly, our results also show that, regardless of dimensionality, the presence of a confining potential can lead to the emergence of typical attributes of critical behavior in the two-state sandpile model, namely, a power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure

Localization for a matrix-valued Anderson model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on L^2(\R)\otimes \C^N, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the F\"urstenberg group of these operators, valid on an interval $I\subset \R$, they exhibit localization properties on $I$, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the F\"urstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters

Shake-up effects and intermolecular tunneling in C60 ions

4 págs.;1 fig.; 3 tabs. ; Rapid CommunicationsThe multiplet structure induced by the Coulomb interactions in C60 n- (n=1-12) is analyzed. The lowest partially occupied molecular orbital gives rise to a set of levels that fill a relatively wide band (2-3 eV). A large (∼1 eV) intramolecular effective repulsion is found. The anions are also shown to be highly polarizable. The optical-absorption and photoemission spectra are calculated. The probability of exciting the molecule upon the addition or removal of one electron is shown to be significant, and this effect may give rise to the insulating behavior of K4C60. The role of intermolecular interactions in suppressing the net repulsion within the C60 molecules is discussed. © 1994 The American Physical Society.Peer Reviewe

A new numerical approach to Anderson (de)localization

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with small disorder allows states that are dynamically delocalized with positive probability. This approach is based on a recent result by Abakumov-Liaw-Poltoratski which is rooted in the study of spectral behavior under rank-one perturbations, and states that every non-zero vector is almost surely cyclic for the singular part of the operator. The numerical work presented is rather simplistic compared to other numerical approaches in the field. Further, this method eliminates effects due to boundary conditions. While we carried out the numerical experiment almost exclusively in the case of the two dimensional discrete random Schroedinger operator, we include the setup for the general class of Anderson models called Anderson-type Hamiltonians. We track the location of the energy when a wave packet initially located at the origin is evolved according to the discrete random Schroedinger operator. This method does not provide new insight on the energy regimes for which diffusion occurs.Comment: 15 pages, 8 figure

Stabilization of internal space in noncommutative multidimensional cosmology

We study the cosmological aspects of a noncommutative, multidimensional universe where the matter source is assumed to be a scalar field which does not commute with the internal scale factor. We show that such noncommutativity results in the internal dimensions being stabilizedComment: 8 pages, 1 figure, to appear in IJMP