Space as a low-temperature regime of graphs

Abstract

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.

22 pages, 12 figures; v3: published version; J.Stat.Phys. 2011

References in corpus (18)

• M Theory As A Matrix Model: A Conjecture
• A Large-N Reduced Model as Superstring
• Spin Foam Models for Quantum Gravity
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Spacetime as a Feynman diagram: the connection formulation
• Quantum Graphity: a model of emergent locality
• Quantum Gravity on the Lattice
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo
• A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime
• Quantum Gravity, or The Art of Building Spacetime
• Causal Dynamical Triangulations and the Quest for Quantum Gravity
• Spin foams as Feynman diagrams
• Statistical Mechanics of Graphity Models
• Single particle in quantum gravity and Braunstein-Ghosh-Severini entropy of a spin network
• Properties of Quantum Graphity at Low Temperature
• Dynamic Multilevel Graph Visualization
• Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
• Matter in Toy Dynamical Geometries

Cited by in corpus (10)

• Emergent Models for Gravity: an Overview of Microscopic Models
• Background independent condensed matter models for quantum gravity
• Experimental Search for Quantum Gravity
• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Statistical mechanics of graph models and their implications for emergent spacetime manifolds
• Disordered locality and Lorentz dispersion relations: an explicit model of quantum foam
• Geometrogenesis under Quantum Graphity: problems with the ripening Universe
• A phase transition creates the geometry of the continuum from discrete space
• Curved geometry and Graphs
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes