Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model

The inhomogeneous six-vertex model is a 2$D$ multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses ${\rm U}(1)$ invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of ${\cal C}$, ${\cal P}$ and ${\cal T}$ as well as translational invariance. The special properties of the lattice system that possesses an additional ${\cal Z}_r$ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.Comment: 29 pages, 2 figures; minor typos fixed, references added, published versio

Scaling limit of the Z2{\cal Z}_2 invariant inhomogeneous six-vertex model

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged ${\rm SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur.Comment: 152 pages, 26 figures, 5 tables, minor misprints correcte

Cardiovascular Risk Reduction with Icosapent Ethyl for Hypertriglyceridemia

BACKGROUND Patients with elevated triglyceride levels are at increased risk for ischemic events. Icosapent ethyl, a highly purified eicosapentaenoic acid ethyl ester, lowers triglyceride levels, but data are needed to determine its effects on ischemic events. METHODS We performed a multicenter, randomized, double-blind, placebo-controlled trial involving patients with established cardiovascular disease or with diabetes and other risk factors, who had been receiving statin therapy and who had a fasting triglyceride level of 135 to 499 mg per deciliter (1.52 to 5.63 mmol per liter) and a low-density lipoprotein cholesterol level of 41 to 100 mg per deciliter (1.06 to 2.59 mmol per liter). The patients were randomly assigned to receive 2 g of icosapent ethyl twice daily (total daily dose, 4 g) or placebo. The primary end point was a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, coronary revascularization, or unstable angina. The key secondary end point was a composite of cardiovascular death, nonfatal myocardial infarction, or nonfatal stroke. RESULTS A total of 8179 patients were enrolled (70.7% for secondary prevention of cardiovascular events) and were followed for a median of 4.9 years. A primary end-point event occurred in 17.2% of the patients in the icosapent ethyl group, as compared with 22.0% of the patients in the placebo group (hazard ratio, 0.75; 95% confidence interval [CI], 0.68 to 0.83; P<0.001); the corresponding rates of the key secondary end point were 11.2% and 14.8% (hazard ratio, 0.74; 95% CI, 0.65 to 0.83; P<0.001). The rates of additional ischemic end points, as assessed according to a prespecified hierarchical schema, were significantly lower in the icosapent ethyl group than in the placebo group, including the rate of cardiovascular death (4.3% vs. 5.2%; hazard ratio, 0.80; 95% CI, 0.66 to 0.98; P=0.03). A larger percentage of patients in the icosapent ethyl group than in the placebo group were hospitalized for atrial fibrillation or flutter (3.1% vs. 2.1%, P=0.004). Serious bleeding events occurred in 2.7% of the patients in the icosapent ethyl group and in 2.1% in the placebo group (P=0.06). CONCLUSIONS Among patients with elevated triglyceride levels despite the use of statins, the risk of ischemic events, including cardiovascular death, was significantly lower among those who received 2 g of icosapent ethyl twice daily than among those who received placebo. (Funded by Amarin Pharma; REDUCE-IT ClinicalTrials.gov number, NCT01492361

Scaling limit of the Z2{\cal Z}_2 invariant inhomogeneous six-vertex model

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged ${\rm SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur

Some algebraic aspects of the inhomogeneous six-vertex model

The inhomogeneous six-vertex model is a 2D multiparametric integrable statistical system. In the scaling limit it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions the model possesses ${\rm U}(1)$ invariance. In this paper we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of ${\cal C}$, ${\cal P}$ and ${\cal T}$ as well as translational invariance. The special properties of the lattice system that possesses an additional ${\cal Z}_r$ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model

Scaling limit of the Z2{\cal Z}_2 invariant inhomogeneous six-vertex model

The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as the powerful analytic technique of the ODE/IQFT correspondence. The results indicate that the critical behaviour of the lattice system is described by the gauged ${\rm SL}(2)$ WZW model with certain boundary and reality conditions imposed on the fields. Our proposal revises and extends the conjectured relation between the lattice system and the Euclidean black hole non-linear sigma model that was made in the 2011 paper of Ikhlef, Jacobsen and Saleur