Low-Dimensional Spin Systems: Hidden Symmetries, Conformal Field Theories and Numerical Checks

We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that have been obtained with a combined use of Conformal Field Theory and of numerical Density Matrix Renormalization Group techniques.Comment: To be published in the proceedings of the XIII Conference on "Symmetries in Physics", held in Bregenz (Voralberg, Austria), 21-24/7/2003. Plain LaTeX2e, 4 EPS figure

Melting of Iron

A theoretical melting curve for iron is determined in the pressure range of the Earth's core by a relation derived from the Ross-Lindemann melting criterium. On this basis the melting point of pure iron is estimated to be about 4800°C at the mantle-core boundary, and 6600°C at the inner core-outer core boundary with a melting point gradient of about 0-8 deglkm

Influence of shell structure on the equation of state of matter at high pressures*

We develop an equation of state of matter in the pressurerange of geophysical interest introducing shell structure in the Thomas-Fermi-Dirac atom model

On the Melting Curve at High Pressures

The asymptotic behaviour of the inclting curves for substances with closepacked structures is analysed by means of Monte Carlo caIculations on model systems of hard spheres. The Kraut--Kennedy melting law does not show the correct asymptotic behaviour. On this basis some recent results on the physics of the Earth's core are rejected

On c=1c=1 critical phases in anisotropic spin-1 chains

Quantum spin-1 chains may develop massless phases in presence of Ising-like and single-ion anisotropies. We have studied c=1 critical phases by means of both analytical techniques, including a mapping of the lattice Hamiltonian onto an O(2) nonlinear sigma model, and a multi-target DMRG algorithm which allows for accurate calculation of excited states. We find excellent quantitative agreement with the theoretical predictions and conclude that a pure Gaussian model, without any orbifold construction, describes correctly the low-energy physics of these critical phases. This combined analysis indicates that the multicritical point at large single-ion anisotropy does not belong to the same universality class as the Takhtajan-Babujian Hamiltonian as claimed in the past. A link between string-order correlation functions and twisting vertex operators, along the c=1 line that ends at this point, is also suggested.Comment: 9 pages, 3 figures, svjour format, submitted to Eur. Phys. J.

Gauge/string duality and scalar glueball mass ratios

It has been shown by Polchinski and Strassler that the scaling of high energy QCD scattering amplitudes can be obtained from string theory. They considered an AdS slice as an approximation for the dual space of a confining gauge theory. Here we use this approximation to estimate in a very simple way the ratios of scalar glueball masses imposing Dirichlet boundary conditions on the string dilaton field. These ratios are in good agreement with the results in the literature. We also find that they do not depend on the size of the slice.Comment: 5 pages, no figures. References updated. Version published in JHE

Stable particles in anisotropic spin-1 chains

Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to the phase boundary where a stable breather exists besides the stable particles, that form the Haldane triplet at the Heisenberg isotropic point. The numerical data, obtained by means of the Density Matrix Renormalization Group, confirm this picture in the so-called large-D phase for which we give also a quantitative analysis of the bound states using standard perturbation theory. However, the situation turns out to be considerably more intricate in the Haldane phase where, to the best of our data, we do not observe stable breathers contrarily to what could be expected from the sine-Gordon model, but rather only the three modes predicted by a novel anisotropic extension of the Non-Linear Sigma Model studied here by means of a saddle-point approximation.Comment: 8 pages, 7 eps figures, svjour clas

Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model

We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries respectively.Comment: 13 pages, RevTeX 4, 12 eps figures, some additional refs. with respect to v1 and citation errors fixe

Unsupervised analysis of small animal dynamic Cerenkov luminescence imaging

Clustering analysis (CA) and principal component analysis (PCA) were applied to dynamic Cerenkov lumi- nescence images (dCLI). In order to investigate the per- formances of the proposed approaches, two distinct dy- namic data sets obtained by injecting mice with 32 P-ATP and 18 F-FDG were acquired using the IVIS 200 optical im- ager. The k-means clustering algorithm has been applied to dCLI and was implemented using interactive data lan- guage 8.1. We show that cluster analysis allows us to ob- tain good agreement between the clustered and the corre- sponding emission regions like the bladder, the liver, and the tumor. We also show a good correspondence between the time activity curves of the different regions obtained by using CA and manual region of interest analysis on dCLIT and PCA images. We conclude that CA provides an auto- matic unsupervised method for the analysis of preclinical dynamic Cerenkov luminescence image data. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE). (DOI: 10.1117/1.3663442