Related papers: Computer Simulations of Causal Sets
In this article we make first steps in coupling matter to causal set theory in the path integral. We explore the case of the Ising model coupled to the 2d discrete Einstein Hilbert action, restricted to the 2d orders. We probe the phase…
The $2$d orders are a sub class of causal sets, which is especially amenable to computer simulations. Past work has shown that the $2$d orders have a first order phase transition between a random and a crystalline phase. When coupling the…
Quantum algorithms offer the potential for significant computational advantages; however, in many cases, it remains unclear how these advantages can be practically realized. Causal Set Theory is a discrete, Lorentz-invariant approach to…
In this paper we will explore two different proposals for the action for causal sets: the Benincasa-Dowker action and a modified version of the chain action. We propose a variational principle for two-dimensional causal sets and use it for…
We modified the recently proposed multicanonical MC algorithm for the case of a magnetic field driven order--order phase transition. We test this {\it multimagnetic} Monte Carlo algorithm for the D=2 Ising model at $\beta=0.5$ and simulate…
Complex systems can be described at myriad different scales, and their causal workings often have multiscale structure (e.g., a computer can be described at the microscale of its hardware circuitry, the mesoscale of its machine code, and…
The Markov chain Monte Carlo method as a statistical mechanics technique for the study of macroscopic systems has furnished the scientific community with great knowledge and advances in the theory of phase transitions. While a number of…
We investigate the phase ordering (pattern formation) of systems of two-dimensional core-shell particles using Monte-Carlo (MC) computer simulations and classical density functional theory (DFT). The particles interact via a pair potential…
We reinvestigate the recently discovered bifurcation phase transition in Causal Dynamical Triangulations (CDT) and provide further evidence that it is a higher order transition. We also investigate the impact of introducing matter in the…
The purpose of this article is to present a detailed numerical study of the second-order phase transition in the 2D Ising model. The importance of correctly presenting elementary theory of phase transitions, computational algorithms and…
We have investigated by molecular dynamics method the influence of a finite number of particles used in computer simulations on fluctuations of thermodynamic properties. As a case study, we used the two-dimensional Lennard-Jones system. 2D…
Causal Dynamical Triangulations (CDT) is a proposal for a theory of quantum gravity, which implements a path-integral quantization of gravity as the continuum limit of a sum over piecewise flat spacetime geometries. We use Monte Carlo…
We adapt Vertex models to understand the physical origin of the formation of long-range ordered structures in repulsive soft particles. The model incorporates contributions from the volume and surface area of each particle. Sampling using…
The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of…
A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is…
The causal set approach to quantum gravity has gained traction over the past three decades, but numerical experiments involving causal sets have been limited to relatively small scales. The software suite presented here provides a new…
Causal set theory provides a model of discrete spacetime in which spacetime events are represented by elements of a causal set---a locally finite, partially ordered set in which the partial order represents the causal relationships between…
We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal models that allow for cycles, latent…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…