Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations
arXiv:1301.1483 · doi:10.1063/1.4808101
Abstract
We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging transfer matrix. In particular, we determine regions in the quadrant of parameters beta, mu >0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.
28 pages, 4 figures, minor changes in main text, title changed, as published
References in corpus (20)
- 2D Gravity and Random Matrices
- Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
- Uniform Infinite Planar Triangulations
- A new perspective on matter coupling in 2d quantum gravity
- A String Field Theory based on Causal Dynamical Triangulations
- Scaling limits of random trees and planar maps
- A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
- Census of Planar Maps: From the One-Matrix Model Solution to a Combinatorial Proof
- The degree distribution in bipartite planar maps: applications to the Ising model
- On the spectral dimension of causal triangulations
- A new continuum limit of matrix models
- Shaken, but not stirred - Potts model coupled to quantum gravity
- Putting a cap on causality violations in CDT
- The Van-der-Waals Gas EOS for the Lorentz Contracted Spheres
- Schramm Loewner Evolution and Liouville Quantum Gravity
- New multicritical matrix models and multicritical 2d CDT
- Quantum Gravity and Matter: Counting Graphs on Causal Dynamical Triangulations
- An Analytical Analysis of CDT Coupled to Dimer-like Matter
- On the Quantum Geometry of Multi-critical CDT
- A note on weak convergence results for uniform infinite causal triangulations
Cited by in corpus (5)
- The Ising model on the random planar causal triangulation: bounds on the critical line and magnetization properties
- Critical behaviour of loop models on causal triangulations
- Conformal Dimensions On Causal Random Geometry
- Potts model coupled to causal triangulations
- Critical region for an Ising model coupled to causal dynamical triangulations