The critical behaviour of Ising spins on 2D Regge lattices

Abstract

We performed a high statistics simulation of Ising spins coupled to 2D quantum gravity on toroidal geometries. The tori were triangulated using the Regge calculus approach and contained up to $512^2$ vertices. We used a constant area ensemble with an added $R^2$ interaction term, employing the $dl/l$ measure. We find clear evidence that the critical exponents of the Ising phase transition are consistent with the static critical exponents and do not depend on the coupling strength of the $R^2$ interaction term. We definitively can exclude for this type of model a behaviour as predicted by Boulatov and Kazakov [Phys. Lett. {\bf B186}, 379 (1987)] for Ising spins coupled to dynamically triangulated surfaces.

15 pages with 3 figures in form of an uudecoded compressed tar-ps-file. FUB-HEP 06/94

References in corpus (4)

• Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study
• Single-Cluster Monte Carlo Study of the Ising Model on Two-Dimensional Random Lattices
• Monte Carlo Study of Topological Defects in the 3D Heisenberg Model
• Ising Model Universality for Two-Dimensional Lattices

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• Simplicial Quantum Gravity on a Randomly Triangulated Sphere
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