20 research outputs found
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