Glauber Dynamics for the mean-field Potts Model

Details Glauber Dynamics for the mean-field Potts Model Glauber Dynamics for the mean-field Potts Model

2012-04-19

arxiv.org/abs/1204.4503v1

Mathematics

Probability

45 pages, 5 figures

Scientific paper

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with $q\geq 3$ states and show that it undergoes a critical slowdown at an inverse-temperature $\beta_s(q)$ strictly lower than the critical $\beta_c(q)$ for uniqueness of the thermodynamic limit. The dynamical critical $\beta_s(q)$ is the spinodal point marking the onset of metastability. We prove that when $\beta<\beta_s(q)$ the mixing time is asymptotically $C(\beta, q) n \log n$ and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order $n$. At $\beta=\beta_s(q)$ the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order $n^{4/3}$. For $\beta>\beta_s(q)$ the mixing time is exponentially large in $n$. Furthermore, as $\beta \uparrow \beta_s$ with $n$, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of $O(n^{-2/3})$ around $\beta_s$. These results form the first complete analysis of the critical slowdown of a dynamics with a first order phase transition.

Affiliated with

Also associated with

No associations

Rating

Glauber Dynamics for the mean-field Potts Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Glauber Dynamics for the mean-field Potts Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Glauber Dynamics for the mean-field Potts Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-5072