Dynamic Critical Behavior of the Chayes-Machta Algorithm for the Random-Cluster Model. I. Two Dimensions

We study, via Monte Carlo simulation, the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts ferromagnet to non-integer q \ge 1. We consider spatial dimension d=2 and 1.25 \le q \le 4 in steps of 0.25, on lattices up to 1024^2, and obtain estimates for the dynamic critical exponent z_{CM}. We present evidence that when 1 \le q \lesssim 1.95 the Ossola-Sokal conjecture z_{CM} \ge \beta/\nu is violated, though we also present plausible fits compatible with this conjecture. We show that the Li-Sokal bound z_{CM} \ge \alpha/\nu is close to being sharp over the entire range 1 \le q \le 4, but is probably non-sharp by a power. As a byproduct of our work, we also obtain evidence concerning the corrections to scaling in static observables.Comment: LaTeX2e, 75 pages including 26 Postscript figure

Comparison of Frequency of Periprocedural Myocardial Infarction in Patients With and Without Diabetes Mellitus to Those With Previously Unknown but Elevated Glycated Hemoglobin Levels (from the TWENTE Trial)

In patients without a history of diabetes mellitus, increased levels of glycated hemoglobin (HbA1c) are associated with higher cardiovascular risk. The relation between undetected diabetes and clinical outcome after percutaneous coronary intervention is unknown. To investigate whether these patients may have an increased risk of periprocedural myocardial infarction (PMI), the most frequent adverse event after percutaneous coronary intervention, we assessed patients of the TWENTE trial (a randomized, controlled, second-generation drug-eluting stent trial) in whom HbA1c data were available. Patients were classified as known diabetics or patients without a history of diabetes who were subdivided into undetected diabetics (HbA1c ≥6.5%) and nondiabetics (HbA1c <6.5%). Systematic measurement of cardiac biomarkers and electrocardiographic assessment were performed. One-year clinical outcome was also compared. Of 626 patients, 44 (7%) were undetected diabetics, 181 (29%) were known diabetics, and 401 (64%) were nondiabetics. In undetected diabetics the PMI rate was higher than in nondiabetics (13.6% vs 3.7%, p = 0.01) and known diabetics (13.6% vs 6.1%, p = 0.11). Multivariate analysis adjusting for covariates confirmed a significantly higher PMI risk in undetected diabetics compared to nondiabetics (odds ratio 6.13, 95% confidence interval 2.07 to 18.13, p = 0.001) and known diabetics (odds ratio 3.73, 95% confidence interval 1.17 to 11.89, p = 0.03). After 1 year, target vessel MI rate was significantly higher in undetected diabetics (p = 0.02) than in nondiabetics, which was related mainly to differences in PMI. Target vessel failure was numerically larger in unknown diabetics than in nondiabetics, but this difference did not reach statistical significance (13.6% vs 8.0%, p = 0.25). In conclusion, undetected diabetics were shown to have an increased risk of PMI