Ising Model Coupled to Three-Dimensional Quantum Gravity

Details Ising Model Coupled to Three-Dimensional Quantum Gravity Ising Model Coupled to Three-Dimensional Quantum Gravity

1992-05-09

arxiv.org/abs/hep-lat/9205009v1

Phys.Rev. D46 (1992) 2480-2485

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages

Scientific paper

10.1103/PhysRevD.46.2480

We have performed Monte Carlo simulations of the Ising model coupled to three-dimensional quantum gravity based on a summation over dynamical triangulations. These were done both in the microcanonical ensemble, with the number of points in the triangulation and the number of Ising spins fixed, and in the grand canoncal ensemble. We have investigated the two possible cases of the spins living on the vertices of the triangulation (``diect'' case) and the spins living in the middle of the tetrahedra (``dual'' case). We observed phase transitions which are probably second order, and found that the dual implementation more effectively couples the spins to the quantum gravity.

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