Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Effect of nesiritide in patients with acute decompensated heart failure

Background Nesiritide is approved in the United States for early relief of dyspnea in patients with acute heart failure. Previous meta-analyses have raised questions regarding renal toxicity and the mortality associated with this agent. Methods We randomly assigned 7141 patients who were hospitalized with acute heart failure to receive either nesiritide or placebo for 24 to 168 hours in addition to standard care. Coprimary end points were the change in dyspnea at 6 and 24 hours, as measured on a 7-point Likert scale, and the composite end point of rehospitalization for heart failure or death within 30 days. Results Patients randomly assigned to nesiritide, as compared with those assigned to placebo, more frequently reported markedly or moderately improved dyspnea at 6 hours (44.5% vs. 42.1%, P = 0.03) and 24 hours (68.2% vs. 66.1%, P = 0.007), but the prespecified level for significance (P≤0.005 for both assessments or P≤0.0025 for either) was not met. The rate of rehospitalization for heart failure or death from any cause within 30 days was 9.4% in the nesiritide group versus 10.1% in the placebo group (absolute difference, −0.7 percentage points; 95% confidence interval [CI], −2.1 to 0.7; P = 0.31). There were no significant differences in rates of death from any cause at 30 days (3.6% with nesiritide vs. 4.0% with placebo; absolute difference, −0.4 percentage points; 95% CI, −1.3 to 0.5) or rates of worsening renal function, defined by more than a 25% decrease in the estimated glomerular filtration rate (31.4% vs. 29.5%; odds ratio, 1.09; 95% CI, 0.98 to 1.21; P = 0.11). Conclusions Nesiritide was not associated with an increase or a decrease in the rate of death and rehospitalization and had a small, nonsignificant effect on dyspnea when used in combination with other therapies. It was not associated with a worsening of renal function, but it was associated with an increase in rates of hypotension. On the basis of these results, nesiritide cannot be recommended for routine use in the broad population of patients with acute heart failure. (Funded by Scios; ClinicalTrials.gov number, NCT00475852.

Cause of Death in Patients With Acute Heart Failure: Insights From RELAX-AHF-2

Objectives: This study sought to better understand the discrepant results of 2 trials of serelaxin on acute heart failure (AHF) and short-term mortality after AHF by analyzing causes of death of patients in the RELAX-AHF-2 (Efficacy, Safety and Tolerability of Serelaxin When Added to Standard Therapy in AHF-2) trial. Background: Patients with AHF continue to suffer significant short-term mortality, but limited systematic analyses of causes of death in this patient population are available. Methods: Adjudicated cause of death of patients in RELAX-AHF-2, a randomized, double-blind, placebo-controlled trial of serelaxin in patients with AHF across the spectrum of ejection fraction (EF), was analyzed. Results: By 180 days of follow-up, 11.5% of patients in RELAX-AHF-2 died, primarily due to heart failure (HF) (38% of all deaths). Unlike RELAX-AHF, there was no apparent effect of treatment with serelaxin on any category of cause of death. Older patients (≥75 years) had higher rates of mortality (14.2% vs. 8.8%) and noncardiovascular (CV) death (27% vs. 19%) compared to younger patients. Patients with preserved EF (≥50%) had lower rates of HF-related mortality (30% vs. 40%) but higher non-CV mortality (36% vs. 20%) compared to patients with reduced EF. Conclusions: Despite previous data suggesting benefit of serelaxin in AHF, treatment with serelaxin was not found to improve overall mortality or have an effect on any category of cause of death in RELAX-AHF-2. Careful adjudication of events in the serelaxin trials showed that older patients and those with preserved EF had fewer deaths from HF or sudden death and more deaths from other CV causes and from noncardiac causes. (Efficacy, Safety and Tolerability of Serelaxin When Added to Standard Therapy in AHF [RELAX-AHF-2]; NCT01870778) © 2020 American College of Cardiology Foundatio