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

Ground states for a class of deterministic spin models with glassy behaviour

We consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the discrete sine Fourier transform. The ground state found by these authors for $N$ odd and $2N+1$ prime is shown to become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes, and to disappear for $N$ even. This last result is based on the explicit construction of a set of eigenvectors for $J$, obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the $2$-torus.Comment: 15 pages, plain LaTe

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.

Deterministic spin models with a glassy phase transition

We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperature expansion. They predict a glassy phase transition at the critical temperature $T\sim 0.8$.Comment: 8 pages, no figures, RevTex forma

Therapy discontinuation or substitution in patients with cardiovascular disease, switching among different products of the same off-patent active substance: a 'real-world' retrospective cohort study

OBJECTIVE: The present study investigated the effects of switching to different products of the same off-patent active substance (brand name or generic) on therapy discontinuation or substitution with another molecule of the same class, in patients with cardiovascular disease treated with statins and antihypertensives in a 'real-world' setting. DESIGN: A retrospective cohort study in a 'real-world' setting. SETTING: Analysis of data performed by integrating administrative databases that included approximately two million individuals who are assisted by the National Health System from three Local Health Units located in three different regions of Italy. PARTICIPANTS: All patients aged 6518\u2005years with at least one prescription of simvastatin, ramipril or amlodipine in the period 1 January to 31 December 2010 were included and followed up for 2\u2005years. MAIN OUTCOME MEASURES: Prescription refills occurring during follow-up were evaluated. Frequency of discontinuation of therapy or substitution with another molecule of the same class (eg, from simvastatin to a different statin) during follow-up was identified. RESULTS: During follow-up, therapy discontinuation or substitution was found to be more frequent in patients switching to a different product of the same active substance compared with non-switching patients (11.5% vs 10.8% and 22.2% vs 20.8% (p=0.002), respectively, in the simvastatin group; 4.0% vs 3.5% and 24.6% vs 22.7% (p<0.001), respectively, in the amlodipine group). In the ramipril group, 8% of patients undertook a therapy substitution to another molecule; no trend towards a lower percentage of substitution was observed in the non-switching group, while 18% of patients discontinued treatment, with a significant difference in favour of patients not switching. These findings were partially confirmed by multivariate analysis. CONCLUSIONS: Switches among products of the same active substance are quite common in patients with cardiovascular disease. Our study suggests that switching may expose patients to a higher risk of therapy discontinuation or substitution

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

Epidemiology of Statin-Treated Patients with Uncontrolled Ldl Levels from Italian Administrative Official Databases

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Scaling of excitations in dimerized and frustrated spin-1/2 chains

We study the finite-size behavior of the low-lying excitations of spin-1/2 Heisenberg chains with dimerization and next-to-nearest neighbors interaction, J_2. The numerical analysis, performed using density-matrix renormalization group, confirms previous exact diagonalization results, and shows that, for different values of the dimerization parameter \delta, the elementary triplet and singlet excitations present a clear scaling behavior in a wide range of \ell=L/\xi (where L is the length of the chain and \xi is the correlation length). At J_2=J_2c, where no logarithmic corrections are present, we compare the numerical results with finite-size predictions for the sine-Gordon model obtained using Luscher's theory. For small \delta we find a very good agreement for \ell > 4 or 7 depending on the excitation considered.Comment: 4 pages, 4 eps figures, RevTeX 4 class, same version as in PR