Geometric effects on critical behaviours of the Ising model

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.Comment: 16 pages, 6 figures, to appear in J. Phys. A: Math. Ge

The dynamic exponent of the Ising model on negatively curved surfaces

We investigate the dynamic critical exponent of the two-dimensional Ising model defined on a curved surface with constant negative curvature. By using the short-time relaxation method, we find a quantitative alteration of the dynamic exponent from the known value for the planar Ising model. This phenomenon is attributed to the fact that the Ising lattices embedded on negatively curved surfaces act as ones in infinite dimensions, thus yielding the dynamic exponent deduced from mean field theory. We further demonstrate that the static critical exponent for the correlation length exhibits the mean field exponent, which agrees with the existing results obtained from canonical Monte Carlo simulations.Comment: 14 pages, 3 figures. to appear in J. Stat. Mec

Periodic boundary conditions on the pseudosphere

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems and we illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.Comment: 30 pages, minor corrections, accepted to J. Phys.

Trajectories of renal biomarkers and new-onset heart failure in the general population:Findings from the PREVEND study

AIMS: Renal dysfunction is one of the most critical risk factors for developing heart failure (HF). However, the association between repeated measures of renal function and incident HF remains unclear. Therefore, this study investigated the longitudinal trajectories of urinary albumin excretion (UAE) and serum creatinine and their association with new-onset HF and all-cause mortality.METHODS AND RESULTS: Using group-based trajectory analysis, we estimated trajectories of UAE and serum creatinine in 6881 participants from the Prevention of Renal and Vascular End-stage Disease (PREVEND) study and their association with new-onset HF and all-cause death during the 11-years of follow-up. Most participants had stable low UAE or serum creatinine. Participants with persistently higher UAE or serum creatinine were older, more often men, and more often had comorbidities, such as diabetes, a previous myocardial infarction or dyslipidaemia. Participants with persistently high UAE had a higher risk of new-onset HF or all-cause mortality, whereas stable serum creatinine trajectories showed a linear association for new-onset HF and no association with all-cause mortality.CONCLUSION: Our population-based study identified different but often stable longitudinal patterns of UAE and serum creatinine. Patients with persistently worse renal function, such as higher UAE or serum creatinine, were at a higher risk of HF or mortality.</p