Ising disks: topology preserving glauber dynamics
Abstract
Abstract We introduce a dynamic model where the state space is the set of contractible cubical sets in the Euclidian space. The permissible state transitions, that is addition and removal of a cube to/from the set, are closest to Eden model with topological constraints, and, we show, are locally decidable . We prove that in the planar special case the state space is connected. We then define a continuous time Markov chain with a fugacity (tendency to grow) parameter. Using the correspondence between our model on the plane and the self-avoiding polygons , we prove that the Markov chain is irreducible (due to state connectivity), and is also ergodic if the fugacity is smaller than a threshold.
Fields of Study & Subjects
Theoretical and Computational Physics
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Journal of Applied and Computational Topology
- Publisher
- Springer Science and Business Media LLC
- Volume
- 10
- Issue
- 3
- Publication date
- 6 July 2026
- Language
- EN