Faculty Advisor
Karl Liechty
Abstract
This paper aims to explore the six-vertex model through simulations designed to investigate the behavior of configurations under specific domain wall boundary conditions. To generate random configurations, we employ the Markov Chain Monte Carlo method while addressing the challenge of mixing times by utilizing the Coupling from the Past (CFTP) algorithm. Implemented in Python, our approach leverages CFTP to ensure exact sampling, avoiding the uncertainty of convergence in traditional Monte Carlo methods. We explore the monotonicity property within this framework and prove that it is only maintained by the steps of this algorithm for very particular values of the parameters.
Recommended Citation
Amir, Malaeka
(2025)
"Exact Sampling of the Six-Vertex Model Using Coupling from the Past,"
DePaul Discoveries: Volume 14, Article 4.
Available at:
https://via.library.depaul.edu/depaul-disc/vol14/iss1/4