Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to 2-d Gravity

Abstract

We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.

7 pages including 5 postscript figures, epsf.sty latex

References in corpus (6)

• World-Sheet Geometry and Baby Universes in 2-D Quantum Gravity
• Baby universes in 2d quantum gravity
• Matter fields with c > 1 coupled to 2d gravity
• Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
• Numerical Study of c>1 Matter Coupled to Quantum Gravity
• A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity

Cited by in corpus (4)

• On the fractal structure of two-dimensional quantum gravity
• Two Ising Models Coupled to 2-Dimensional Gravity
• Percolation on Strings and the Cover-up of the c=1 Disaster
• Square Gravity