Related papers: Lattice Models of Random Geometries
In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…
I review recent progress in simplicial quantum gravity in three and four dimensions, in particular new results on the phase structure of modified models of dynamical triangulations, the application of a strong-coupling expansion, and the…
Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…
We review recent work in the lattice approach to random surfaces and quantum gravity. Our task is made somewhat easier by some very interesting results, particularly in four dimensions, that have appeared recently and which are reported…
The paper concerns lattice triangulations, that is, triangulations of the integer points in a polygon in $\mathbb{R}^2$ whose vertices are also integer points. Lattice triangulations have been studied extensively both as geometric objects…
We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean…
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…
A polymer folding model on the square lattice is constructed with attractive contact interactions of strength 1/c^2, 0<c<1. The corresponding model on a dynamical random lattice, with freely fluctuating co-ordination number at each vertex,…
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
A simple lattice gas model with random fields and gravity is introduced to describe a system of grains moving in a disordered environment. Off equilibrium relaxations of bulk density and its two time correlation functions are numerically…
We consider the four-dimensional Euclidean dynamical triangulations lattice model of quantum gravity based on triangulations of $S^{4}$. We couple it minimally to a scalar field in the quenched approximation. Our results suggest a…
Motivated by recent experiments on objects moved vertically through a bed a glass beads, a simple model to study granular drag is proposed. The model consists of dimers on a slanted two-dimensional lattice through which objects are dragged…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
In this paper we introduce a new model of random simplicial complexes depending on multiple probability parameters. This model includes the well-known Linial - Meshulam random simplicial complexes and random clique complexes as special…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
We briefly overview the development of Euclidean quantum gravity in four dimensions regarded as a branch of statistical mechanics of discretized random manifolds.
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…