Universality in the 2d Quasi-periodic Ising Model and Harris-Luck Irrelevance.

We prove that in the 2D Ising model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case; that is, the critical exponents for the specific heat and energy-energy correlations are identical, and no logarithmic corrections are present. The disorder produces a quasi-periodic modulation of the amplitude of the correlations and a renormalization of the velocities, that is, the coefficients of the rescaling of positions, and of the critical temperature. The result establishes the validity of the prediction based on the Harris-Luck criterion, and it provides the first rigorous proof of universality in the Ising model in the presence of quasi-periodic disorder in both directions and for any angle.

Anomaly Non-renormalization in Interacting Weyl Semimetals.

Weyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of 'Weyl nodes'. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in dimensions. We consider a class of interacting 3D lattice models for Weyl semimetals and prove that the quadratic response of the quasi-particle flow between the Weyl nodes is universal, that is, independent of the interaction strength and form.

Quantization of the Interacting Hall Conductivity in the Critical Regime.

The Haldane model is a paradigmatic 2 lattice model exhibiting the integer quantum Hall effect. We consider an interacting version of the model, and prove that for short-range interactions, smaller than the bandwidth, the Hall conductivity is quantized, for all the values of the parameters outside two critical curves, across which the model undergoes a 'topological' phase transition: the Hall coefficient remains integer and constant as long as we continuously deform the parameters without crossing the curves; when this happens, the Hall coefficient jumps abruptly to a different integer. Previous works were limited to the perturbative regime, in which the interaction is much smaller than the bare gap, so they were restricted to regions far from the critical lines.

Sex differences in the efficacy of antihypertensive treatment in preventing cardiovascular outcomes and reducing blood pressure: protocol for a systematic review and meta-analysis.

Introduction: Hypertension is a leading cause of mortality worldwide and its prevalence is expected to rise over the next decade. Sex differences exist in the epidemiology and pathophysiology of hypertension. It is well established that antihypertensive treatment can significantly reduce the risk for stroke and other cardiovascular disease events.

Implementation and Effectiveness of Coaching for Surgeons in Practice - A Mixed Studies Systematic Review.

Introduction: Despite recent changes to medical education, surgical training remains largely based on the apprenticeship model. However, after completing training, there are few structured learning opportunities available for surgeons in practice to refine their skills or acquire new skills. Personalized observation with feedback is rarely a feature of traditional continuing medical education learning.

Localization of Interacting Fermions in the Aubry-André Model.

We consider interacting electrons in a one-dimensional lattice with an incommensurate Aubry-André potential in the regime when the single-particle eigenstates are localized. We rigorously establish the persistence of ground state localization in the presence of weak many-body interaction, for almost all the chemical potentials. The proof uses a quantum many-body extension of methods adopted for the stability of tori of nearly integrable Hamiltonian systems and relies on number-theoretic properties of the potential incommensurate frequency.

Conductivity in the Heisenberg chain with next-to-nearest-neighbor interaction.

We consider a spin chain given by the XXZ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a system has an ideal metallic behavior (infinite conductivity), by rigorously establishing strict lower bounds on the zero-temperature Drude weight, which are strictly positive. The proof is based on exact renormalization group methods allowing us to prove the convergence of the expansions and to fully take into account the irrelevant terms, which play an essential role in ensuring the correct lattice symmetries.

Universal relations for nonsolvable statistical models.

We present the first rigorous derivation of a number of universal relations for a class of models with continuously varying indices (among which are interacting planar Ising models, quantum spin chains and 1D Fermi systems), for which an exact solution is not known, except in a few special cases. Most of these formulas were conjectured by Luther and Peschel, Kadanoff, and Haldane, but only checked in the special solvable models; one of them, related to the anisotropic Ashkin-Teller model, is novel.

Anomalous critical exponents in the anisotropic Ashkin-Teller model.

We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when the isotropic limit is reached. We prove that, even in the region where universality for the specific heat holds, anomalous critical exponents appear: for instance, we predict the existence of a previously unknown anomalous exponent, continuously varying with the strength of the interaction, describing how the difference between the critical temperatures rescales with the anisotropy parameter.