Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models

We demonstrate that the invaded cluster algorithm, recently introduced by Machta et al, is a fast and reliable tool for determining the critical temperature and the magnetic critical exponent of periodic and aperiodic ferromagnetic Ising models in two dimensions. The algorithm is shown to reproduce the known values of the critical temperature on various periodic and quasiperiodic graphs with an accuracy of more than three significant digits. On two quasiperiodic graphs which were not investigated in this respect before, the twelvefold symmetric square-triangle tiling and the tenfold symmetric T\"ubingen triangle tiling, we determine the critical temperature. Furthermore, a generalization of the algorithm to non-identical coupling strengths is presented and applied to a class of Ising models on the Labyrinth tiling. For generic cases in which the heuristic Harris-Luck criterion predicts deviations from the Onsager universality class, we find a magnetic critical exponent different from the Onsager value. But also notable exceptions to the criterion are found which consist not only of the exactly solvable cases, in agreement with a recent exact result, but also of the self-dual ones and maybe more.Comment: 15 pages, 5 figures; v2: Fig. 5b replaced, minor change

Symmetries and reversing symmetries of toral automorphisms

Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their connection with unit groups in orders of algebraic number fields. For the question of reversibility, we derive necessary conditions in terms of the characteristic polynomial and the polynomial invariants. We also briefly discuss extensions to (reversing) symmetries within affine transformations, to PGL(n,Z) matrices, and to the more general setting of integer matrices beyond the unimodular ones.Comment: 34 page

Compilation on Synthesis, Characterization and Properties of Silicon and Boron Carbonitride Films

During the last years the interest in silicon and boron carbonitrides developed remarkably. This interest is mainly based on the extraordinary properties, expected from theoretical considerations. In this time significant improvements were made in the synthesis of silicon carbonitride SiCxNy and boron carbonitride BCxNy films by both physical and chemical methods. In the Si–C–N and B-C-N ternary systems a set of phases is situated, namely diamond, SiC, -Si3N4, c-BN, B4C, and -C3N4, which have important practical applications. SiCxNy has drawn considerable interest due to its excellent new properties in comparison with the Si3N4 and SiC binary phases. The silicon carbonitride coatings are of importance because they can potentially be used in wear and corrosion protection, high-temperature oxidation resistance, as a good moisture barrier for high-temperature industrial as well as strategic applications. Their properties are low electrical conductivity, high hardness, a low friction coefficient, high photosensitivity in the UV region, and good field emission characteristics. All these characteristics have led to a rapid increase in research activities on the synthesis of SiCxNy compounds. In addition to these properties, low density and good thermal shock resistance are very important requirements for future aerospace and automobile parts applications to enhance the performance of the components. SiCxNy is also an important material in micro- and nano-electronics and sensor technologies due to its excellent mechanical and electrical properties. The material possesses good optical transmittance properties. This is very useful for membrane applications, where the support of such films is required (Fainer et al., 2007, 2008; Mishra, 2009; Wrobel, et al., 2007, 2010; Kroke et al., 2000). The structural similarity between the allotropic forms of carbon and boron nitride (hexagonal BN and graphite, cubic BN and diamond), and the fact that B-N pairs are isoelectronic to C-C pairs, was the basis for predictions of the existence of ternary BCxNy compounds with notable properties (Samsonov et al., 1962; Liu et al., 1989; Lambrecht & Segall, 1993; Zhang et al., 2004). This prediction has stimulated intensive research in the last 40 years towards the synthesis of ternary boron carbonitride. BCxNy compounds are interesting in both the cubic (c-BCN) and hexagonal (h-BCN) structure. On the one hand, the ..

Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension 2 and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps.Comment: 29 pages, 3 figure

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating functions for the number of coincidence site lattices and coincidence isometries, for specific examples.Comment: 10 pages, 1 figure; paper presented at Aperiodic 2009 (Liverpool

Error Thresholds on Dynamic Fittness-Landscapes

In this paper we investigate error-thresholds on dynamics fitness-landscapes. We show that there exists both lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error-threshold present on a static landscape. The upper error-threshold is a new limit that only exists on dynamic fitness-landscapes. We also show that for long genomes on highly dynamic fitness-landscapes there exists a lower bound on the selection pressure needed to enable effective selection of genomes with superior fitness independent of mutation rates, i.e., there are distinct limits to the evolutionary parameters in dynamic environments.Comment: 5 page

On rotational excitations and axial deformations of BPS monopoles and Julia-Zee dyons

It is shown that Julia-Zee dyons do not admit slowly rotating excitations. This is achieved by investigating the complete set of stationary excitations which can give rise to non-vanishing angular momentum. The relevant zero modes are parametrized in a gauge invariant way and analyzed by means of a harmonic decomposition. Since general arguments show that the solutions to the linearized Bogomol'nyi equations cannot contribute to the angular momentum, the relevant modes are governed by a set of electric and a set of non self-dual magnetic perturbation equations. The absence of axial dipole deformations is also established.Comment: 22 pages, Revtex, no figure

Critical domain walls in the Ashkin-Teller model

We study the fractal properties of interfaces in the 2d Ashkin-Teller model. The fractal dimension of the symmetric interfaces is calculated along the critical line of the model in the interval between the Ising and the four-states Potts models. Using Schramm's formula for crossing probabilities we show that such interfaces can not be related to the simple SLE$_\kappa$, except for the Ising point. The same calculation on non-symmetric interfaces is performed at the four-states Potts model: the fractal dimension is compatible with the result coming from Schramm's formula, and we expect a simple SLE$_\kappa$ in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial changes in the data production, analysis and in the conclusions. Added a section about the crossing probability. Typeset with 'iopart