Triangular Trimers on the Triangular Lattice: an Exact Solution

A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated by rigid domain walls. The transfer matrix can be diagonalised by a Bethe Ansatz with two types of particles. This leads two an exact expression for the entropy on a two-dimensional subset of the parameter space.Comment: 4 pages, REVTeX, 5 EPS figure

Stably uniform affinoids are sheafy

We develop some of the foundations of affinoid pre-adic spaces without Noetherian or finiteness hypotheses. We give some explicit examples of non-adic affinoid pre-adic spaces (including a locally perfectoid one). On the positive side, we also show that if every affinoid subspace of an affinoid pre-adic space is uniform, then the structure presheaf is a sheaf; note in particular that we assume no finiteness hypotheses on our rings here. One can use our result to give a new proof that the spectrum of a perfectoid algebra is an adic space.Comment: Version 2 of the manuscript -- the arguments are now presented for general f-adic rings with a topologically nilpotent unit (the original proofs still go through in this generality

Bethe Ansatz solution of triangular trimers on the triangular lattice

Details are presented of a recently announced exact solution of a model consisting of triangular trimers covering the triangular lattice. The solution involves a coordinate Bethe Ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model, due to M. Widom and P. A. Kalugin. The connection of the trimer model with related solvable models is discussed.Comment: 33 pages, LaTeX2e, 13 EPS figures, PSFra

Three-phase point in a binary hard-core lattice model?

Using Monte Carlo simulation, Van Duijneveldt and Lekkerkerker [Phys. Rev. Lett. 71, 4264 (1993)] found gas-liquid-solid behaviour in a simple two-dimensional lattice model with two types of hard particles. The same model is studied here by means of numerical transfer matrix calculations, focusing on the finite size scaling of the gaps between the largest few eigenvalues. No evidence for a gas-liquid transition is found. We discuss the relation of the model with a solvable RSOS model of which the states obey the same exclusion rules. Finally, a detailed analysis of the relation with the dilute three-state Potts model strongly supports the tricritical point rather than a three-phase point.Comment: 17 pages, LaTeX2e, 13 EPS figure

Microbial diversity and biogeochemical cycling in soda lakes

Soda lakes contain high concentrations of sodium carbonates resulting in a stable elevated pH, which provide a unique habitat to a rich diversity of haloalkaliphilic bacteria and archaea. Both cultivation-dependent and -independent methods have aided the identification of key processes and genes in the microbially mediated carbon, nitrogen, and sulfur biogeochemical cycles in soda lakes. In order to survive in this extreme environment, haloalkaliphiles have developed various bioenergetic and structural adaptations to maintain pH homeostasis and intracellular osmotic pressure. The cultivation of a handful of strains has led to the isolation of a number of extremozymes, which allow the cell to perform enzymatic reactions at these extreme conditions. These enzymes potentially contribute to biotechnological applications. In addition, microbial species active in the sulfur cycle can be used for sulfur remediation purposes. Future research should combine both innovative culture methods and state-of-the-art ‘meta-omic’ techniques to gain a comprehensive understanding of the microbes that flourish in these extreme environments and the processes they mediate. Coupling the biogeochemical C, N, and S cycles and identifying where each process takes place on a spatial and temporal scale could unravel the interspecies relationships and thereby reveal more about the ecosystem dynamics of these enigmatic extreme environments

Anomalous Finite-Size Scaling in a Critical Lattice Model

Introduction Consider a two-dimensional statistical mechanical model and put it on an infinite cylinder of circumference L. In the thermodynamic limit L ! 1 the free energy per unit length F L approaches f 1 L, where f 1 is the bulk free energy per unit area. For isotropic critical twodimensional systems conformal invariance predicts [1, 2] F L = f 1 L \Gamma ßc 6 L \Gamma1 + o(L \Gamma1 ); (1) with c the so-called central charge. Similar scaling is expected when the system can be made isotropic by an affine transformation. Here we discuss a simple model that exhibits anomalous scaling F L = f 1 L \Gamma const<F48.3