Name
Abstract | ||
|---|---|---|
We study the Glauber dynamics for the random cluster (FK) model on the torus (Z/nZ)2 with parameters (p,q), for q is an element of (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(logn) for p not equal p(c) to a power-law in n at p = p(c). This was verified at p not equal p(c) by Blanca and Sinclair, whereas at the critical p = p(c), with the exception of the special integer points q = 2,3,4 (where the model corresponds to the Ising/Potts models) the best-known upper bound on mixing was exponential in n. Here we prove an upper bound of nO(logn) at p = p(c) for all q is an element of (1,4], where a key ingredient is bounding the number of nested long-range crossings at criticality. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1002/rsa.20868 | RANDOM STRUCTURES & ALGORITHMS |
Keywords | Field | DocType |
critical phenomena,Glauber dynamics,mixing time,random cluster model | Discrete mathematics,Quasi-polynomial,Pure mathematics,Critical phenomena,Mathematics | Journal |
Volume | Issue | ISSN |
56.0 | 2.0 | 1042-9832 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Reza Gheissari | 1 | 0 | 0.34 |
| Eyal Lubetzky | 2 | 355 | 28.87 |