The F model on dynamical quadrangulations

Abstract

The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation are adapted to the problem of these dynamical quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a series of extensive Monte Carlo simulations and accompanying finite-size scaling analyses, we investigate the critical behaviour of the 6-vertex F model coupled to the ensemble of dynamical quadrangulations and determine the matter related as well as the graph related critical exponents of the model.

LaTeX, 43 pages, 10 figures, 7 tables; substantially shortened and revised version as published, for more details refer to V1, to be found at http://arxiv.org/abs/hep-lat/0409028v1

References in corpus (40)

• String Theory and Noncommutative Geometry
• The Loop Algorithm
• A Short Survey of Noncommutative Geometry
• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• On the fractal structure of two-dimensional quantum gravity
• Scaling in quantum gravity
• Multicritical Phases of the O(n) Model on a Random Lattice
• World-Sheet Geometry and Baby Universes in 2-D Quantum Gravity
• String Field Theory of Noncritical Strings
• Construction of Non-critical String Field Theory by Transfer Matrix Formalism in Dynamical Triangulation
• How far are we from the quantum theory of gravity?
• Baby universes in 2d quantum gravity
• Exact Solution of the Six-Vertex Model on a Random Lattice
• String Field Theory of $c\le 1$ Noncritical Strings
• Lorentzian 3d Gravity with Wormholes via Matrix Models
• Logarithmic Corrections in the 2D XY Model
• Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
• Quantum geometry of 2d gravity coupled to unitary matter
• Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity
• A scenario for the c>1 barrier in non-critical bosonic strings
• Two-Matrix model with ABAB interaction
• A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity
• The Harris-Luck criterion for random lattices
• Crossing the c=1 barrier in 2d Lorentzian quantum gravity
• The six-vertex model on random lattices
• New critical phenomena in 2d quantum gravity
• The quantum space-time of c=-2 gravity
• Quantum geometry of topological gravity
• Effective Sampling of Random Surfaces by Baby Universe Surgery
• The Weingarten Model a la Polyakov
• The square-lattice F model revisited: a loop-cluster update scaling study
• Connected Correlators in Quantum Gravity
• Counting planar diagrams with various restrictions
• Ising (anti-)ferromagnet on dynamical triangulations and quadrangulations
• The asymmetric ABAB matrix model
• Square Gravity
• Search for Scaling Dimensions for Random Surfaces with c=1
• The Quantum Spacetime of c>0 2d Gravity
• The XY Model Coupled to Two-Dimensional Quantum Gravity
• On the Universality of Matrix Models for Random Surfaces

Cited by in corpus (4)

• Frustration effects in antiferromagnets on planar random graphs
• The square-lattice F model revisited: a loop-cluster update scaling study
• Power laws in zero-range processes on random networks
• Geometric and Stochastic Clusters of Gravitating Potts Models