Year: 2023
Type: preprint
Abstract: We study the mixing time of systematic scan Glauber dynamics Ising model on the complete graph. On the complete graph $K_n$, at each time, $k \leq n$ vertices are chosen uniformly random and are updated one by one according to the uniformly randomly chosen permutations over the $k$ vertices. We show that if $k = o(n^{1/3})$, the high temperature regime $β< 1$ exhibits cutoff phenomena. For critical temperature regime $β= 1$, We prove that the mixing time is of order $n^{3/2}k^{-1}$. For $β> 1$, we prove the mixing time is of order $nk^{-1}\log n$ under the restricted dynamics.
Source: arXiv (Cornell University)
Author: Jeon, Sanghak
Institution: Princeton University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4384920052