Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics   The Swendsen-Wang dynamics is a Markov chain widely used by physicists to
sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer,
Frieze and Rue proved that on the complete graph K_n the mixing time of the
chain is at most O(n^{1/2}) for all non-critical temperatures. In this paper we
show that the mixing time is Theta(1) in high temperatures, Theta(log n) in low
temperatures and Theta(n^{1/4}) at criticality. We also provide an upper bound
of O(log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts
model on any tree with n vertices.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs