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

Inorganic carbon acquisition in red-tide dinoflagellates

Carbon acquisition was investigated in three marine bloom-forming dinoflagellates – Prorocentrum minimum, Heterocapsa triquetra and Ceratium lineatum. In vivo activities of extracellular and intracellular carbonic anhydrase (CA), photosynthetic O2 evolution, CO2 and HCO3– uptake rates were measured by membrane inlet mass spectrometry (MIMS) in cells acclimated to low pH (8.0) and high pH (8.5 or 9.1). A second approach used short-term 14C-disequilibrium incubations to estimate the carbon source utilized by the cells. All three species showed negligible extracellular CA (eCA) activity in cells acclimated to low pH and only slightly higher activity when acclimated to high pH. Intracellular CA (iCA) activity was present in all three species, but it increased only in P. minimum with increasing pH. Half-saturation concentrations (K1/2) for photosynthetic O2 evolution were low compared to ribulose 1,5-bisphosphate carboxylase/oxygenase (Rubisco) kinetics. Moreover, apparent affinities for inorganic carbon (Ci) increased with increasing pH in the acclimation, indicating the operation of an efficient CO2 concentration mechanism (CCM) in these dinoflagellates. Rates of CO2 uptake were comparably low and could not support the observed rates of photosynthesis. Consequently, rates of HCO3– uptake were high in the investigated species, contributing more than 80% of the photosynthetic carbon fixation. The affinity for HCO3– and maximum uptake rates increased under higher pH. The strong preference for HCO3– was also confirmed by the 14C-disequilibrium technique. Modes of carbon acquisition were consistent with the 13C-fractionation pattern observed and indicated a strong species-specific difference in leakage. These results suggest that photosynthesis in marine dinoflagellates is not limited by Ci even at high pH, which may occur during red tides in coastal waters