We establish how the Breitenlohner-Freedman (BF) bound is realized on tilings of two-dimensional Euclidean Anti-de Sitter space. For continuum, BF states that spaces, fluctuation modes remain stable for small negative mass squared m^{2}. This follows from a real and positive total energy gravitational system. finite cutoff ϵ, we solve Klein-Gordon equation numerically regular hyperbolic tilings. When ϵ→0, find continuum approached in manner independent tiling. confirm these results via...

Context. Due to the ever increasing number of observations during past decades, Type Ia supernovae are nowadays regarded as a heterogeneous class optical transients consisting several subtypes. One largest these subclasses is Iax supernovae. They have been suggested originate from pure deflagrations in carbon-oxygen Chandrasekhar mass white dwarfs because outcome this explosion scenario general agreement with their subluminous nature. Aims. Although few deflagration studies already carried...

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in Poincaré disk model. Using highly optimized, efficient algorithms, tilings with millions vertices can be created matter minutes on single workstation computer. Facilities including computation adjacent vertices, dynamic lattice manipulation, refinements, as well powerful plotting animation capabilities are provided to support advanced uses graphs. In this...

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in Poincaré disk model. Using highly optimized, efficient algorithms, tilings with millions vertices can be created matter minutes on single workstation computer. Facilities including computation adjacent vertices, dynamic lattice manipulation, refinements, as well powerful plotting animation capabilities are provided to support advanced uses graphs. In this...

In 1974, Harris proposed his celebrated criterion: Continuous phase transitions in $d$-dimensional systems are stable against quenched spatial randomness whenever $d\ensuremath{\nu}>2$, where $\ensuremath{\nu}$ is the clean critical exponent of correlation length. Forty years later, motivated by violations criterion for certain lattices such as Voronoi-Delaunay triangulations random point clouds, Barghathi and Vojta put forth a modified topologically disordered systems:...

We study the two-dimensional Ising model on a network with novel type of quenched topological (connectivity) disorder. construct random lattices constant coordination number and perform large scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. find disorder-dependent effective exponents, similar diluted models, showing thus no clear universal behavior. Considering very recent results for proximity graphs correlation analysis suggested by...

The authors present an algorithm for constructing constant coordination lattices -- topologically disordered spatial graphs with number that are significantly faster than comparable proximity graph constructions. As application, the paper shows numerically 3D Ising model on these belongs to clean universality class.

The Voronoi construction is ubiquitous across the natural sciences and engineering. In statistical mechanics, however, only its dual, Delaunay triangulation, has been considered in investigation of critical phenomena. this paper we set to fill gap by studying three prominent systems classical equilibrium spin-1/2 Ising model, nonequilibrium contact process, conserved stochastic sandpile model on two-dimensional random graphs. Particular motivation comes from fact that these graphs have...

Despite decades of research, the precise role topological disorder in critical phenomena has yet to be fully understood. A major contribution been work by Barghathi and Vojta, which uses spatial correlations explain puzzling earlier results. However, due its reliance on coordination number fluctuations, their criterion cannot applied constant-coordination lattices, raising question, for classes transitions this type can a relevant perturbation. In order cast light we investigate...

Self-similar dynamical processes are characterized by a growing length scale $ξ$ which increases with time as $ξ\sim t^{1/z}$, where z is the exponent. The best known example simple random walk z=2. Usually such assumed to take place on static background. In this paper we address question what changes if background itself evolves dynamically. As an consider isotropically and homogeneously inflating space. For exponentially fast expansion it turns out that self-similar properties of...

Hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in Poincar\'e disk model. Using highly optimized, efficient algorithms, tilings with millions vertices can be created matter minutes on single workstation computer. Facilities including computation adjacent vertices, dynamic lattice manipulation, refinements, as well powerful plotting animation capabilities are provided to support advanced uses graphs. In this...

We propose a generalized diffusion equation for flat Euclidean space subjected to continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent factors $a(t)\sim t^\lambda$ and \exp(\mu t)$, partial differential is solved analytically asymptotic scaling behavior, as well dynamical exponents, are derived. Whereas in case two processes (diffusion expansion) compete crossover observed, we find that dynamics...

We establish how the Breitenlohner-Freedman (BF) bound is realized on tilings of two-dimensional Euclidean Anti-de Sitter space. For continuum, BF states that spaces, fluctuation modes remain stable for small negative mass-squared $m^2$. This follows from a real and positive total energy gravitational system. finite cutoff $\varepsilon$, we solve Klein-Gordon equation numerically regular hyperbolic tilings. When $\varepsilon\to0$, find continuum approached in manner independent tiling....

Clearly, in nature, but also technological applications, complex systems built an entirely ordered and regular fashion are the exception rather than rule. In this thesis we explore how critical phenomena influenced by quenched spatial randomness. Specifically, consider physical undergoing a continuous phase transition presence of topological disorder, where underlying structure, on which system evolves, is given non-regular, discrete lattice. We therefore endeavour to achieve thorough...