Corpus ID: 26261692

Quasi-polynomial mixing of critical 2D random cluster models

@article{Gheissari2016QuasipolynomialMO,
  title={Quasi-polynomial mixing of critical 2D random cluster models},
  author={Reza Gheissari and Eyal Lubetzky},
  journal={arXiv: Probability},
  year={2016}
}
We study the Glauber dynamics for the random cluster (FK) model on the torus $(\mathbb{Z}/n\mathbb{Z})^2$ with parameters $(p,q)$, for $q \in (1,4]$ and $p$ the critical point $p_c$. The dynamics is believed to undergo a critical slowdown, with its continuous-time mixing time transitioning from $O(\log n)$ for $p\neq p_c$ to a power-law in $n$ at $p=p_c$. This was verified at $p\neq p_c$ by Blanca and Sinclair, whereas at the critical $p=p_c$, with the exception of the special integer points $q… Expand

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