Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.Comment: 6 pages, REVTeX

Refactoring Process Models in Large Process Repositories.

With the increasing adoption of process-aware information systems (PAIS), large process model repositories have emerged. Over time respective models have to be re-aligned to the real-world business processes through customization or adaptation. This bears the risk that model redundancies are introduced and complexity is increased. If no continuous investment is made in keeping models simple, changes are becoming increasingly costly and error-prone. Though refactoring techniques are widely used in software engineering to address related problems, this does not yet constitute state-of-the art in business process management. Process designers either have to refactor process models by hand or cannot apply respective techniques at all. This paper proposes a set of behaviour-preserving techniques for refactoring large process repositories. This enables process designers to eectively deal with model complexity by making process models better understandable and easier to maintain

Entropy of chains placed on the square lattice

We obtain the entropy of flexible linear chains composed of M monomers placed on the square lattice using a transfer matrix approach. An excluded volume interaction is included by considering the chains to be self-and mutually avoiding, and a fraction rho of the sites are occupied by monomers. We solve the problem exactly on stripes of increasing width m and then extrapolate our results to the two-dimensional limit to infinity using finite-size scaling. The extrapolated results for several finite values of M and in the polymer limit M to infinity for the cases where all lattice sites are occupied (rho=1) and for the partially filled case rho<1 are compared with earlier results. These results are exact for dimers (M=2) and full occupation (\rho=1) and derived from series expansions, mean-field like approximations, and transfer matrix calculations for some other cases. For small values of M, as well as for the polymer limit M to infinity, rather precise estimates of the entropy are obtained.Comment: 6 pages, 7 figure

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Kosterlitz Thouless Universality in Dimer Models

Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that this universality class is unaffected even in the large N limit. This shows that the mean field analysis often used in this limit breaks down in the critical region.Comment: 4 pages, 4 figure

Network development in biological gels: role in lymphatic vessel development

In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801–808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the Cahn–Hilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model

Phase diagram of the one-dimensional extended attractive Hubbard model for large nearest-neighbor repulsion

We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff} can be mapped onto two XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422 and U<-4, singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in BaKBiO.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

On Ising and dimer models in two and three dimensions

Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher's mapping of two dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagetic Ising model maps onto a non-symmetry breaking transition in dimer language -- instead it becomes a deconfinement transition for test monomers. Next, we introduce a modification of Fisher's mapping in which a second dimer model, also equivalent to the Ising model, is defined on a generically different lattice derived from the dual. In contrast to Fisher's original mapping, this enables us to reformulate frustrated Ising models as dimer models with positive weights and we illustrate this by providing a new solution of the fully frustrated Ising model on the square lattice. Finally, by means of the modified mapping we show that a large class of three-dimensional Ising models are precisely equivalent, in the time continuum limit, to particular quantum dimer models. As Ising models in three dimensions are dual to Ising gauge theories, this further yields an exact map between the latter and the quantum dimer models. The paramagnetic phase in Ising language maps onto a deconfined, topologically ordered phase in the dimer models. Using this set of ideas, we also construct an exactly soluble quantum eight vertex model.Comment: 10 pages, 9 figures autmatically include